Nonequilibrium pulsed femtosecond semiconductor disk laser

ABSTRACT

A surface-emitting semiconductor laser system contains at least one MQW unit of at least three constituent QWs, axially separated from one another substantially non-equidistantly. The MQW unit is located within the axial extent covered, in operation of the laser, by a half-cycle of the standing wave of the field at a wavelength within the gain spectrum of the gain medium; immediately neighboring nodes of the standing wave are on opposite sides of the MQW unit. So-configured MQW unit can be repeated multiple times and/or complemented with individual QWs disposed outside of the half-cycle of the standing wave with which such MQW unit is associated. The semiconductor laser further includes a pump source configured to input energy in the semiconductor gain medium and a mode-locking element to initiate mode-locking.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority from and benefit of the U.S.Provisional Applications No. 62/321,911 filed on Apr. 13, 2016, and No.62/393,439 filed on Sep. 12, 2016.

The present application is also a continuation-in-part of U.S. patentapplication Ser. No. 14/847,908, filed Sep. 8, 2015 and published asU.S. 2016/0087407, which in turn claims priority from and benefit ofU.S. Provisional Patent Applications No. 62/053,557 filed on Sep. 22,2014 and No. 62/054,083 filed on Sep. 23, 2014.

The disclosure of each of the above-identified patent documents isincorporated by reference herein in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with government support under Grant No.FA9550-14-1-0062 awarded by USAF/FOSR. The government has certain rightsin the invention.

TECHNICAL FIELD

The present invention is related to a semiconductor gain medium havingquantum well layers, and more general to a semiconductor gain mediumhaving multiple quantum well structure including quantum wells placedaway from the antinodes of a cavity standing wave formed at the centralwavelength.

BACKGROUND

High-power, high-brightness continuous wave (CW) and mode-locked lasersremain of interest to the research community. The use of semiconductorlasers for this purpose provides well-recognized advantages, not theleast of which are cost efficiency and ease of handling, in practice. Aconventional approach to achieving high laser power outputs from thesemiconductor lasers is to utilize a so-called resonant periodic gain(RPG) structure, which includes a multiplicity of sequentially-disposedquantum wells (QWs) limited on one side by a distributed Bragg grating(DBR) reflector and, on the other side, an optical window through whichlaser emission is delivered outside of the cavity. The optical windowsometimes includes anti-reflectance and/or high-reflectance (AR/HR) orother thin-film optical coatings, terminating the cavity at theinterface with the ambient medium (such as air). A schematic diagramillustrating such structure is shown in FIG. 1.

While some of the highest power outputs have been demonstrated with theuse of such structures (for example, outputs greater than 100 Watts oftotal power; or 15 Watts for a single-mode narrow-linewidth poweroutput; or about 5 Watts of output via 680-femtosecond duration pulses),practice and related art clearly demonstrate that theRPG-structure-based lasers prove to be quite inefficient in achievingshort-pulsed laser operation—for example, in generation of a train ofpulses with durations below 100 fs—let alone in generation of sub-100 fspulses at high average power. While some attempts to reach the pulsedoperation (with 100 fs pulses) have been made, the problem of unreliablestability of such operation, caused by depletion of excited carriers atsubstantially single optical frequency, has not been resolved.

Given that operationally-stable sub-100 fs pulsed lasing with high gain(at high power levels) remains of interest in a multitude ofapplications (including medicine, biology, sampling/probing of ultrafastprocesses, and fast optical data communications, to name just a few),there remains a need in a semiconductor laser configuration that differsfrom the conventional RPG configuration to overcome the existingproblems.

SUMMARY

Embodiments of the invention provide a surface-emitting semiconductorlaser system configured to operate in a mode-locked regime. The lasersystem includes a) an optical resonator having an optical axis; b) asemiconductor laser chip; and c) a pump source. The semiconductor laserchip is disposed within the optical resonator and contains asemiconductor gain medium that is characterized by a gain spectrum. Thegain spectrum has a bandwidth that includes a first wavelength. The gainmedium has a first multiple quantum well (MQW) unit, which first MQWunit is defined by a sequence of at least three first quantum wells(QWs) separated from one another substantially non-equidistantly. Thepump source is in operable communication with said laser chip and isconfigured to pump energy to the semiconductor gain medium to produceexcited-state carriers in the first MQW unit. The laser chip isconfigured to form a standing wave within said chip at a frequency ofthe first wavelength, such standing wave having first and secondimmediately neighboring nodes located along the optical axis within thegain medium, which nodes are formed on the opposite sides of said firstMQW unit.

Embodiments of the invention further provide a method for generatingsub-100 fs pulses with the use of such semiconductor laser system.

BRIEF DESCRIPTION OF THE DRAWINGS

The following disclosure will be better understood in reference to thefollowing accompanying generally not-to-scale Drawings, of which:

FIG. 1 shows a schematic of a prior art implementation of a mode-lockedsemiconductor disk laser (VECSEL) consisting of a multiple quantum wellresonant-periodic-gain (RPG) active structure with each quantum wellplaced near the anti-node of the standing wave field (vertical bars near6 μm and 7 μm) on the left and a semiconductor saturable absorber mirror(SESAM) consisting of a single quantum well (QW) and a partiallytransmitting mirror (vertical line) on the far right, not shown to theleft of the RPG region is a highly reflecting semiconductor distributedBragg reflector (DBR) consisting of multiple repeats of a pair ofsemiconductor materials (for example, AlAs/GaAs pairs);

FIG. 2 shows a schematic of an implementation of a modified conventionalRPG arrangement in which the QWs are configured to optimize the amountof pump light absorbed and broaden the net linear gain;

FIG. 3 shows a schematic of an implementation of a gain medium having amultiple quantum well gain architecture having 10 QWs spaced by 10nanometers packed inside a single field anti-node, wherein the otherlayers to the right are a standard cap layer to prevent carrier leakageand an anti-reflection (AR) coating;

FIG. 4A is a schematic diagram illustrating an implementation of a gainmedium having a multiple quantum well gain architecture having 10 QWs(spaced by 10 nanometers) that are packed inside a single fieldanti-node; the other layers shown to the right of the QWs are a standardcap layer (configured to prevent carrier leakage) and an anti-reflection(AR) coating. Standing waves corresponding to a central wavelength, ashort and long wavelengths are also shown;

FIG. 4B shows plots representing the multiple QW (MQW) structure of FIG.4A, including the full linear gain spectrum (lower solid line 4B.1), theabsorption curve of the single QW saturable absorber (upper solid line,4B2), and the net gain curve (representing the difference between thefull linear gain spectrum curve and the absorption curve; shown as adashed curve 4B4). Also shown is the modelocked pulse bandwidth (upperdashed curve, 4B.3), that has a bandwidth greater than that of the netgain;

FIG. 5A shows a plot of the linear gain, SESAM absorption, and theirdifference for an initial inversion n^(qw)=3×10¹⁶ m⁻² corresponding tothe embodiment shown in FIG. 1; parameters are provided in the inset;

FIG. 5B shows a plot of the linear gain, SESAM absorption, and theirdifference for an initial inversion n^(qw)=3×10¹⁶ m⁻² corresponding tothe embodiment of FIG. 3; parameters are given in the inset;

FIG. 6 presents plots of the dynamic evolution of the pulse peak in themode-locked cavity for three implementations of an RPG structure RPG-6,RPG-8, RPG-10 (containing, respectively, 6, 8 and 10 QWs) and for threeimplementations of an MQW structure MQW-6, MQW-8, MQW-10 (with 6, 8, 10QWs, respectively);

FIG. 7 shows a schematic of an implementation of a conventional 10 QWRPG structure with a single QW located between twoimmediately-neighboring nodes of the field;

FIG. 8 shows a schematic of an implementation of a MQW structure with 10QWs packed at sub-wavelength spacing into a single half-cycle (halfperiod) of the intracavity field;

FIG. 9 shows a plot of the transient temporal behavior (before stablemode locking is realized) of the RPG structure and the MQW structuretowards a stable mode-locked state, once in this state the initialinversion for each structure is systematically decremented initiallytowards a net gain of zero for RPG and for the MQW; after the gaindepletion the inversion is decremented further entering the netabsorption region until such a point that the mode-locking is lost andthe system returns to the CW lasing state, the sets of curves for theMQW structure on the right show that mode-locking is sustained well intothe net linear absorption region;

FIG. 10 shows a plot of linear gain as a function of carrier density ofthe RPG structure for the densities the dynamics of which are shown inFIG. 9 and displayed in the inset, the upper curve shows the absorptionof the SESAM for each of the cases;

FIG. 11 shows a plot of linear gain as a function of carrier density ofthe MQW structure for the densities the dynamic of which are shown inFIG. 9 and displayed in the inset, the upper curve is the fixed SESAMabsorption for each case;

FIG. 12 shows a plot of snapshots, representing inversion depletion atparticular moments in time, for the RPG structure as the pulse sweepsthrough the gain chip, wherein the initial Fermi distribution ofcarriers for the inverted system is shown at time t=0 for reference;

FIG. 13 shows a plot of snapshots of the inversion depletion for the 8:8MQW structure as the pulse sweeps through the gain chip, wherein theinitial Fermi distribution of carriers for the inverted system is shownat time t=0 for reference;

FIG. 14 shows plots of pulse energy (measured in pJ) for the RPG and MQWstructures of FIGS. 7 and 8; the MQW structure delivers much higherpulse energies than the RPG up to 80 pJ. The presented simulationresults are just above threshold (corresponding to the situation whenthe gain just compensates the loss) so the pulse energies are low;

FIG. 15 shows plots of mode-locked pulse peak amplitudes for the MQWstructure with 10, 8 and 6 QWs packed in a single half-cycle of thestanding wave field between two immediately neighboring nodes of thestanding wave field;

FIG. 16 shows plots of mode-locked pulse energies for the MQW structurewith 10, 8 and 6 QWs packed in a single half-cycle of the standing wavefield between two immediately neighboring nodes of the standing wavefield;

FIG. 17 shows a schematic of an implementation of a MQW arrangementwhere a 5 QW unit cell is replicated to produce a 5:5 structure;

FIG. 18 shows the final mode-locked pulse (that is, stable pulse thatregenerates itself in each round trip in the cavity) of duration ofabout 86 fs resulting from the structure in FIG. 17 and the phase acrossthe pulse indicates some residual chirp;

FIG. 19 shows a schematic of an embodiment of an extension of the 5:5MQW structure of FIG. 17. Here, the remaining space in the structure isfilled with additional QWs;

FIG. 20 shows the final mode-locked pulse of the structure in FIG. 19,where the pulse duration is 83 fs and the phase across the pulse has aresidual chirp;

FIG. 21 shows a schematic of an implementation containing an 8:8 MQWstructure where 8 QWs are packed within each half cycle of fieldintensity distribution along the optical axis;

FIG. 22 illustrates a mode-locked pulse corresponding to the structureof FIG. 21, with a pulse duration of about 43 fs and a weak chirp;

FIG. 23 shows a schematic of an implementation of a 10 QW MQW structureat a center wavelength of 1200 nm, where 10 QWs are densely packedwithin a single field half-cycle;

FIG. 24 shows a plot of field strength and phase of mode-locked pulsesof 84 fs duration generated by the structure of FIG. 23;

FIG. 25 shows a schematic of an implementation of a 60-QW-containing MQWstructure with 10 QWs per standing-wave field half-cycle;

FIG. 26 shows a plot of field strength and phase of mode-locked pulse of205 fs duration generated from the structure of FIG. 25 with a weakchirp;

FIG. 27 shows a schematic of an implementation of an MQW structurecontaining 10 QWs with QW thicknesses and spacing reduced such as toaccommodate more spectral bandwidth for more effective depletion ofcarriers;

FIG. 28 shows plots of the linear gain spectrum (line 28.1) for highinversion and high SESAM absorption (line 28.2) as well as the netlinear gain (line 28.3), relevant material parameters are given in thefigure inset;

FIG. 29 shows plots representing respectively an amplitude an phase of amode-locked 23.8 fs pulse with weak chirp across the pulse;

FIG. 30 shows the spectrum of the pulse of FIG. 29, which spectrumextends beyond the linear net gain bandwidth (line 28.3 of FIG. 28); theshaded region indicates the extension of the linear net gain spectrum;

FIG. 31 shows a schematic of a related implementation of the10-QW-containing MQW structure of FIG. 27, but with QW thicknesses andspacings reduced so as to accommodate more spectral bandwidth for moreeffective depletion of carriers;

FIG. 32 shows plots of the linear gain spectrum (line 32.1) for lowerinversion and high SESAM absorption (line 32.2), as well as the netlinear gain curve (line 32.3) for the 10 QW-containing MQW structure (ofeither FIG. 27, or FIG. 31); here, the linear gain (line 32.1) isreduced relative to that shown in FIG. 28 while the SESAM absorption(line 32.2) is kept the same, which results in a smaller and muchnarrower net gain spectrum as compared to that of FIG. 28 (line 32.3 vsline 28.3);

FIG. 33 includes plots of calculated amplitude and phase distribution ofa mode-locked 32.4 fs pulse, produced by an embodiment of the invention,with a substantially constant phase across the duration of the pulse;

FIG. 34 shows the spectrum of the pulse of FIG. 33, which spectrumextends far beyond the linear net gain bandwidth (line 32.3 of FIG. 32);the shaded region indicates the narrow width of the linear net gainspectrum;

FIG. 35 shows distributions of the linear gain (line 35.1), SESAMabsorption (line 35.2) and net linear gain (line 35.3) in a case wherethe carrier density is reduced from 5×10¹⁶ m⁻² to 4.5×10¹⁶ m⁻²; for thestructure of FIG. 27;

FIG. 36 shows the distributions of linear gain (line 36.1), SESAMabsorption (line 36.2) and net linear gain (line 36.3) for the situationwhere the outcoupling loss is increased for 1.5% to 2%, for thestructure of FIG. 27;

FIG. 37 is a plot representing the spectrum of the final mode-lockedpulse corresponding the semiconductor gain medium if the presentinvention with characteristics shown in FIG. 35; the shaded regiondenotes the net linear gain bandwidth;

FIG. 38 shows the spectrum of the final mode-locked pulse correspondingthe semiconductor gain medium if the present invention withcharacteristics shown in FIG. 36; the shaded region denotes the netlinear gain bandwidth;

FIG. 39 provides plots representing amplitude and phase of themode-locked pulse of duration 27.0 fs, which pulse corresponds to anembodiment of the invention represented by FIGS. 35 and 37;

FIG. 40 provides plots representing the mode-locked pulse of duration28.1 fs, which pulse corresponds to an embodiment of the inventionrepresented by FIGS. 36 and 38;

FIG. 41 is a schematic diagram of a layout of an externaloptically-pumped V-cavity for generating mode-locked pulse trains;

FIG. 42 shows a plot of experimentally measured autocorrelation of thesub-picosecond mode-locked high average power pulse obtained with theuse of a V-cavity configured according to the schematic of FIG. 41;

FIG. 43 shows an optical scheme (for use with an embodiment of theinvention) for pumping of the barrier with a large quantum defectΔE=(ℏω_(p)−ℏω), the external optical-pump photon energy is ℏω_(p) and ℏωdenotes the generated laser photon energy;

FIG. 44 shows an optical scheme (for use with an embodiment of theinvention) for pumping of the quantum well with a much smaller quantumdefect ΔE=(ℏω_(p)−ℏω), the external optical pump photon energy is ℏω_(p)and ℏω denotes the generated laser photon energy;

FIG. 45 is a schematic diagram of a multi-pass optical system configuredfor optical pumping of a thin disk crystal; an identical optical systemcould be used for both barrier and QW-pumped VECSELs (the energydiagrams of which are shown in FIGS. 43 and 44, respectively);

FIG. 46 shows a schematic diagram of an MQW laser chip mounted on arectangular CVD diamond heat sink with the latter being bonded to acopper heat sink disk, to increase the efficiency of heat removal fromthe semiconductor chip;

FIG. 47 shows an implementation of an electrically pumped MQWsemiconductor disk laser configured according to an embodiment of theinvention, where the “active region” depicts the location of the MQWchip, and the DBR layers are doped to facilitate the flow of carriersfrom the contact regions;

FIG. 48 illustrates a gain region of a VECSEL chip of an embodiment ofthe invention that utilizes 2 MQWs having 4 QWS each;

FIG. 49 shows a simulated output pulse of the structure of FIG. 48 in alinear cavity with SESAM and output coupler;

FIG. 50 shows plots illustrating accumulated strain for different gainregion designs for the 4+4 QW structure (plot A), a structure with 2+4+4QWs (plot B), and a 6 QW structure (plot C). The accumulated strain isgiven in % nm expressing the accumulated strain effect for a structurewhere the material with thickness (x nm) is strained by (y %) relativeto its substrate; % strain=[(lattice constant material a)−(latticeconstant material b)]/[average lattice constant].

FIG. 51A is an image of photoluminescence produced by the chip grownaccording to the structure of FIG. 48, showing pronounced dark linedislocations. The illuminated spot is on the order of 400 μm, which is atypical pump spot size;

FIG. 51B is an image of FIG. 51A that is enhanced with lines drawn totrave the dislocations of FIG. 51A for better visibility;

FIG. 52 is a schematic diagram of a VECSEL gain region configuredaccording to a “121-121” embodiment of MQW units;

FIG. 53 shows a simulated output pulse produced by the chip utilizingthe MQW structure of FIG. 52 in a linear cavity with SESAM and outputcoupler;

FIG. 54 is a diagram of a VECSEL gain region configured according to a“1-121-121” embodiment of MQW units;

FIG. 55 shows a simulated output pulse of the chip utilizing the MQWstructure of FIG. 54 in a linear cavity with SESAM and output coupler;

FIG. 56 shows the accumulated strain in gain structures of FIGS. 52 and54;

FIG. 57 is a photoluminescence image of the MQW “1-121-121” chip of FIG.54 evidencing the absence of dark line dislocations, incontradistinction with that of FIG. 51. The illuminated spot is on theorder of 400 μm, which is a typical pump spot size;

FIG. 58 is a diagram of a VECSEL gain region configured according to a“1-121-121-121” embodiment of MQW units;

FIG. 59 shows a simulated output pulse of the chip utilizing the MQWstructure of FIG. 58 in a linear cavity with SESAM and output coupler;

FIGS. 60 and 61 illustrate, respectively, the gain portion of the VECSELstructure and the calculated mode-locked pulse parameters of anembodiment the symmetry of the gain structure of which is “broken” ormodified as compared to that of the embodiment of FIG. 54;

FIGS. 62 and 63 illustrate, respectively, the related embodiment of thegain portion of the VECSEL structure and the calculated mode-lockedpulse parameters of an embodiment the symmetry of the gain structure ofwhich is modified as compared to that of the embodiment of FIG. 54;

FIGS. 64 and 65 illustrate, respectively, yet another related embodimentof the gain portion of the VECSEL structure and the calculatedmode-locked pulse parameters of an embodiment the symmetry of the gainstructure of which is modified as compared to that of the embodiment ofFIG. 54;

FIG. 66 is a diagram of a VECSEL gain region configured according to a“1-121-121” QW and additionally enhanced with specific auxiliary layerson right hand side of the gain region to provide AR coating configuredto flatten and minimize the group delay dispersion that is exhibited bythe chip in operation;

FIG. 67 illustrates a portion of the VECSEL structure of FIG. 66, withalternative capping and AR-layers.

FIGS. 68A, 68B illustrate portions of one SESAM embodiment for use witha VECSEL structure containing MQW units withnon-equidistantly-placed-QWs, configured according to an idea of theinvention.

FIGS. 69 and 70 show plots illustrating the comparison of amplificationachieved in three different active gain regions, each containing adifferent QW arrangement as discussed in reference to FIGS. 71, 72, 73,74, and 75.

FIG. 71 illustrates a conventional 12-period QW RPG structure;

FIG. 72 illustrates an MQW-unit-based structure of the invention withconstituent QWs being spaced equidistantly;

FIG. 73 illustrates an MQW-unit-based structure of the invention withconstituent QWs in each MQW unit being spaced equidistantly andadditionally containing a gain-boosting QW near the signal DBR mirror;

FIG. 74 illustrates an MQW-unit-based structure of the invention withconstituent QWs is each MQW unit being spaced non-equidistantly;

FIG. 75 illustrates an MQW-unit-based structure of the invention withconstituent QWs in each MQW unit being spaced non-equidistantly andadditionally containing a gain-boosting QW near the signal DBR mirror.

Generally, the sizes and relative scales of elements in Drawings may beset to be different from actual ones to appropriately facilitatesimplicity, clarity, and understanding of the Drawings. For the samereason, not all elements present in one Drawing may necessarily be shownin another.

DETAILED DESCRIPTION

Referring again to FIG. 1, a conventionally-utilized in related art RPGstructure is configured such that amplification of light (caused byappropriately pumping the RPG-structure-containing semiconductor laser)occurs at substantially only a single frequency. Put differently,conventional RPG structures are designed such as to deliver an outputhaving as high a power as possible. Accordingly, the idea behind theconventional RPG structure, utilized by related art to date, is toutilize the most gain through resonant growth of the internal(intracavity) field through multiple passes within the shortsemiconductor micro-cavity of the semiconductor chip. To achieve this inoperation, a given RPG structure is configured such that, when there isformed a standing electromagnetic wave within the laser cavity, ahalf-cycle of such standing wave (marked as 110 in FIG. 1) covers orembraces only one QW (such that the anti-node of the correspondingelectrical field distribution is located at or near the QW(s) inquestion).

The characteristic carrier-carrier scattering time in the gain region ofsemiconductor MQW systems is in the range of 100 fs. Since these carrierscatterings lead to a replenishment of the gain in the spectral regionof the pulse, they cause an elongation of the pulse. Therefore, theinterest is to form pulses with a sub-100 fs duration such that thepulse-lengthening influence of carrier scattering is minimized and/orcan be neglected.

The impact of sub-100 fs mode-locked semiconductor disk laser sources isdifficult to overestimate across a wide spectrum of applications suchas, for example, medicine and biology (multiphoton cell imaging,minimally invasive subcellular nanosurgery), sensor applications, andgeneration of frequency combs. The ability to generate stableultra-short pulse trains (<100 fs) using compact and reliablesemiconductor devices is expected to enable a new generation of sourcesat targeted wavelengths not directly accessible with the use ofcurrently employed Ti:sapphire or doped fiber lasers. The highrepetition rates achievable with semiconductor sources are particularlyuseful for LIDAR, optical arbitrary wave-form generation, advancedultra-high bandwidth communication systems, and coherent detectionapplications. Semiconductor disk laser sources in particular have beenshown to exhibit very good quantum-limited noise performance, especiallycompared to doped fiber laser counter-parts. Such low noise performancein a compact mode-locked high-repetition rate (1 to 10 GHz) source couldprove to be the ideal frequency comb source and for further powerscaling such high repetition sources via fiber amplification.Applications include improved and field-usable clocks and ultra-lownoise microwave generation for improved timing and synchronization incommunication, navigation, and guidance systems.

Attempts to reach 100 fs duration fundamental mode-locked pulses have sofar not been successful with RPG structures: the shortest durationdemonstrated to-date is around 200 fs at low average power. In referenceto FIG. 2, to shorten the duration of a pulse in an RPG-structureconfiguration, an attempt has been made to change the conventionalstructure of FIG. 1 to ensure that some anti-nodes (such as anti-node202, for example) are unpopulated while other individual antinodes (suchas antinodes 206, 208, 210) overlap with either one or two QWs 212. Thisapproach, discussed by P. Klopp, U. Griebner, M. Zorn and M. Weyers, (in“Pulse repetition rate of 92 GHz or pulse duration shorter than 110 fsfrom a mode-locked semiconductor disk laser” APL, 98, 071103, 2011),resulted in a very low average power output 107 fs pulse mode-lockingregime of operation, and could, in principle, be utilized in the lowgain limit. (For the purposes of this disclosure, the term “low gainlimit” implies that the gain (the amplification of the pulse) per roundtrip to be very weak, for example in the percentage range. This leads torather weak pulses that do not replete the inversion.)

In the low-gain limit, the structure proposed by Klopp et al. yieldsmode-locked pulses the bandwidth of which utilizes the bandwidth of thecurve representing net linear gain (provided by a given semiconductorgain medium) and approaches the sought-after target of 100 fs-durationpulses, does so without any concern for stability of the pulsed-laseroperation. Indeed, the stability of the demonstrated pulsed operationremains a generally unresolved issue, as stable pulses are realized onlyunder low gain conditions (where only a small fraction of availablecarriers are used).

It is well recognized that, when pumped harder, the operation of thedevice of Knopp and similar RPG-based devices tend to selectively removecarriers from only a relatively narrow spectral region (the width ofwhich is comparable, similar or is approximately equal to the width ofthe band of the net linear gain) until such pumping bleaches out thecarriers in a very narrow, limited spectral window; the effect oftenreferred to in the art as spectral hole burning. Pumping at everincreasing levels leads amplification of light outside of the initialspectrally-pumped region and causes a multiplicity of generallyuncorrelated pulses at different optical frequencies and/or stronglychirped pulses, which is recognized as an undesirable result.Embodiments of the present invention provide the desired solutions. Forthe purposes of this disclosure, weak pumping implies that the system isjust barely above threshold (whatever a threshold may be for theparticular device), while harder pumping implies that one increases thepumping in the range of tens of percent.

In the presently provided solution, the distribution of quantum-wells inthe gain medium of the laser system is judiciously defined to avoid orat least mitigate the effect of spectral hole burning and, as a result,the effect is achieved of using the exited-state carried at frequenciesof the majority of the available full gain spectrum, thereby leading tosubstantial shortening of pulses in a mode-locked operation of the lasersystem, reliably and repeatably, beyond the sought-after limit of 100fs. In addition, in some cases, the reduction or even elimination ofpulse chirping is also demonstrated.

A persisting problem of inability of existing semiconductor-based laserstructures to generate a train of sub-100 fs duration pulses, whichtrain remains operationally stable at different levels of gain is solvedby utilizing a semiconductor laser the gain medium of which isconfigured to include one or more multiple quantum well (MQW) units,each of which is structured to contain at least three individual quantumwells (QWs). The at least three QWs of a given MQW unit are spaced fromone another, along an axis perpendicular to such QWs, by a distance thatis shorter than that corresponding to a reference wavelength (in onecase, a wavelength from the gain spectrum characterizing thesemiconductor gain medium at hand).

In doing so, the semiconductor gain medium is structured such that (whenpumped by a judiciously chosen pump source) the immediately neighboringnodes of a standing wave created through the gain medium are formed onopposite sides of a given MQW unit. The term “standing wave” is referredto a wave in a medium, in which each point on the axis of the wave hasan associated constant amplitude. The locations at which the amplitudeis minimum are referred to as nodes, and the locations where theamplitude is maximum are called antinodes.

A goal of achieving a spectrally- and temporally stable (at variouslevels of gain) mode-locked operation of a semiconductor laser withpulse durations below 100 fs is achieved by configuring thesemiconductor gain medium inside an optical resonator to include atleast one MQW unit that, on one hand, has at least three constituent QWsand, on the other hand, the spatial extent of which along an opticalaxis preferably but optionally exceeds a distance corresponding to aquarter-of-a-cycle of a standing wave formed by an electric fieldthroughout the gain medium when the latter is pumped by an appropriatepump source to cause lasing.

A problem of inability of the existing semiconductor lasers to operatein a mode-locked regime characterized by high-power, stable pulses withdurations below 100 fs at different levels of pumping the gain medium issolved by structuring the multiple QWs in the gain medium such thatamplification of light (with the use carriers excited by the pump power)is effectuated within an operational spectral bandwidth that, on onehand, exceeds the bandwidth of the net-gain curve characterizing thegain medium and, on the other hand, is a subset of a bandwidth of thefill-gain curve characterizing such gain medium.

Embodiments of the invention demonstrate that the use of a semiconductorgain medium containing judiciously configured MQW structure(s) overcomesthe problem of strong chirping of pulses produced by a conventional RPGstructure, and allows for a realization of an ultrashort (<100 fs)pulsed mode-locked laser operation.

According to the idea of the invention, the gain medium (in whichmode-locking is initiated via a phase transition) is designed to includesub-wavelength spaced three or more quantum wells forming at least onegroup of densely packed QWs (referred to as a MQW unit) at a judiciouslychosen location along the optical axis in the thin active semiconductorsection of the resulting laser system. Such location is defined tocorrespond to a space between two immediately neighboring nodes of astanding-wave formed by an electrical field at a frequency from the gainspectrum characterizing the gain medium (for example, at a frequencycorresponding to the central portion of the gain spectrum, referred toas a central frequency) as a result of external pumping thereof withenergy. So structured, the gain medium drives a nonlinear phasetransition that sweeps out most of the carriers, defined in thesemiconductor electron-hole plasma within the full gain spectrum. One ormore of MQW units in optional combination with any additional QWs,created in the semiconductor gain medium at hand, form and defined whatis referred to as a cumulative MQW structure of an embodiment of theinvention. In an MQW unit of the resulting cumulative MQW structure atleast some of individual QWs are offset from the nearest antinode of thestanding wave pattern (for example, some of the offset QWs can bepositioned approximately midway between the node and antinode of thestanding wave pattern as shown in the examples of FIGS. 3 and 17 below,or closer to a node than to an antinode of the standing wave pattern asshown in the examples of FIGS. 4A and 8).

One of optional but operationally advantageous features of aconfiguration of the cumulative MQW structure of the invention is that,in a laser oscillator, the individual QWs are stacked in a sequence andspaced apart by sub-wavelength distances to effectuate, during theoperation, the use of most if not all of the inversion in thesemiconductor electron/hole plasma to form, in a mode-locked regime, atrain of pulses with ultrashort duration (<100 fs), high peak andaverage power, and high energy. The sub-wavelength spacing of theindividual quantum wells in an MQW unit is preferred to promote a strongcoherent emission of a giant pulse of very short duration and, in aspecific case, having a substantially spectrally—lat phase front(resulting in no chirp) as the pulse builds up over multiple passesaround the optical resonator of the laser system of the embodiment. Itwill be recognized by a skilled artisan that phase-locked sub-wavelengthspaced QW emitters that have been packed, as a group, between the twoimmediately-neighboring nodes of the field distribution formed along theoptical axis of the semiconductor chip during the operation, produce, incooperation, laser emission that saturates at much higher intensitiesthan a standard resonant-periodic-gain (RPG) structure.

Related art methodologies used for design of QW-based semiconductorstructure (such as, for example an RPG structure) are turning on anddepend exclusively on utilizing the net linear gain of a givensemiconductor medium (which linear gain is defined by a differencebetween the full linear gain and the semiconductor saturable absorberloss). The use of the net linear gain characteristic(s) provides thebasis for estimation of the duration of the mode-locked pulses producedby the resulting laser, with no consideration to non-linear optimizationwhatsoever. The present invention stems from the recognition that suchnet linear gain approach provides for reasonable estimation of operationof the laser system only in the low gain limit, far away from the strongpumping regime where carriers are typically bleached out. In thislimited situation, the spectrum of a generated pulse is very narrow,which inevitably defines a pulse of long duration typically wellexceeding 100 femtoseconds. A reader is referred to discussion ofmode-locking regime of operation of a laser system utilizing RPGstructures, presented by J. V Moloney, I. Kilen, A. Bäumner, M.Scheller, and S. W. Koch, Nonequilibrium and thermal effects inmode-locked VECSELs, Opt. Express, 22, (6) 6422 (2014), incorporatedherein in by reference in its entirety,

In stark contradistinction with the systems and method of the relatedart, the initial strategy for defining the locations and parameters ofindividual QWs of the cumulative MQW structure of an embodiment of theinvention is based on assessment of the bandwidth of the full lineargain spectrum at a reference carrier density for which the system isinverted (and is, therefore, capable of laser emission). According tothe idea of the invention, for a semiconductor gain medium with chosenparameters individual QWs are initially positioned at such locationsinside such gain medium as to that maximally extract carriers (and,consequently, generate photons) across the majority—and, in a specificcase—full span of the spectral bandwidth of the available gain. As shownbelow, even such initial, linear approach to the determination of thelocations of the individual QWs of the cumulative MQW structure of theembodiments of the invention already provides asubstantially-superior—as compared with the results achieved by relatedart—operational characteristics of the laser system of the invention ina mode-locking regime, which includes sought-after sub-100-fs durationsof pulses and reduced chirping.

However, to improve the structure of the laser chip even further, suchinitial arrangement strategy is optionally additionally optimized withthe use of a full non-linear optimization algorithm, whereby the fullnonequilibrium Semiconductor Bloch equations (SBE) coupled to theMaxwell equations describing light propagation in the laser cavity aresolved directly. (Full details of the underlying theory can be found inH. Haug, and S. W. Koch. Quantum theory of the optical and electronicproperties of semiconductors. World scientific, 2009, which isincorporated herein by reference in its entirety.) For additionaldetails, the reader is referred to I. Kilen, J. Hader, J. V Moloney, andS. W. Koch, Ultrafast Nonequilibrium Carrier Dynamics in SemiconductorLaser Mode-Locking, Optica (2014), incorporated herein in by referencein its entirety.

General

In the simulations discussed below (which were carried out for both theRPG structure and various embodiments of the cumulative MQW structuresof the invention, the full cavity length was considered to be about 3.2centimeters (to simplify the computational complexity of resolving theinteracting microscopic many-body electron-hole system). In thefollowing description, most of the parameters used in the simulationsare listed as insets in related figures. Parameters not listed in thismanner are otherwise explicitly provided. Except as otherwise stated,the simulation assumed an output coupling of 2%, a light roundtrip timeof 21 picoseconds (corresponding to the 3.212 cm cavity length), asaturable absorber recovery time of 0.5 ps, and a QW recovery time inthe active chip of 30 ps. However, the final simulation observationsreproduced the observed mode-locking behavior of more complex differentlength linear, v-shaped and z-shaped cavities for example.

Referring now to the drawings, wherein like reference numerals designateidentical or corresponding parts throughout the several views, FIG. 1schematically illustrates a conventional RPG-structure-containing lasercavity arranged to produce a train of mode-locked pulses via passivemode-locking. The break denoted as 110 just beyond 7.5 microns signifiesa free space gap between the RPG structure 120 on the left of FIG. 1 andSESAM structure 130 on the right of the Figure. This non-limitingexample of a conventional RPG-based laser structure is chosen tosimplify already complex many-body simulations. In FIG. 1 (also in FIGS.2-4, 7, 8, 17, 19, 21, 23, 25, 27, and 31) the index of refraction ofvarious layers are indicated by the inverted “L” shaped lines, such aslines 140A, 140B for example. The line in the shape of an absolute valueof a sine wave (such as line 150 of FIG. 1, for example) represents thein-cavity standing wave of the electric field. The vertical bars (suchas bars 160 of FIG. 1) represent groupings of one or more quantum wells(QWs)—a narrow line representing a single QW (for example, lines 212near 5.95 and 6.2 microns in FIG. 2) and a wider line or grouped linesrepresenting multiple QWs (for example, double lines 212 near 6.4 mm inFIG. 2).

As seen from the FIGS. 1 and 2, in a conventional RPG-structure-basedsemiconductor laser, the resonant and anti-resonant periodic gainstructures and other variants of these have arrangements that focus onplacement of one (and maybe two) individual QW (s) at anti-node of astanding-wave formed in the laser a central wavelength of operation.Conventionally, there may be multiple half-wavelength repeats ofso-configured QW structures (for example, the 10 repeats shown in FIG.1), each with one (possibly two or none of) QWs placed near each halfwavelength peak. The faithfulness and adherence of related art to theRPG arrangement is quite understandable—it proved to be successful inachieving record high power performance for continuous wave (CW) beams,resulting from the advantage of the structure in achieving near optimalgain at a very narrow range of wavelengths by placing individual QWs atfield maxima in the standing wave pattern within the semiconductor chip.At the same time, however, this very cause of the high-power operationof an RPG structure inevitably and critically limits its spectralperformance, both in terms of utilization of gain spectrum and theduration of the resulting pulses.

In contrast to conventional RPG based semiconductor lasers, thecumulative MQW structure configured according to embodiment of thepresent invention is capable of and effective in generating gain acrossthe entire available gain bandwidth of the active region of thesemiconductor medium. By generating photons effectively across theentire available gain bandwidth, all or most of the carriers in theelectron-hole subsystem are utilized—which is not achieved at all bystructured of related art—with the result of light amplification acrossthe optimized, often maximum possible, frequency bandwidth.

Such unexpected result is enabled by packing at least three—andpreferably more—QWs with subwavelength at locations (along the opticalaxis) that fall under a half-cycle of the standing wave fieldoscillation. So configured QWs, although tightly packed with thinbarriers, typically have the individual QW electron and hole groundstate wavefunctions decoupled. Another possible arrangement would havethe QWs be so tightly spatially packed as to comprise a superlatticestructure—in this case, the electron and hole quantum wavefunctions aredelocalized across the QW stack instead of being decoupled. Table 1provides an example, for illustration, of arrangement of a cumulativeMQW structure configured according to the idea of the invention.

TABLE 1 Parameters (such as number of repeats, material thicknesses innanometers, material types and compositions and refractive indices) fora specific example of an embodiment of a barrier pumped MQW structurecontaining two repeats of 5 QWs placed around 2 standing wave fieldanti-nodes. It is assumed that the pump wavelength is 808 nm and thelaser wavelength is 980 nm. Material Repeats Thickness [nm]GaAs-substrate n_(r) 1 155.40 In_(0.49)Ga_(0.51)P 3.1954 1 34.00GaAs_(0.90)P_(0.10) 3.4607 5 2.50 GaAs_(0.90)P_(0.10) 3.4607 8.00In_(0.155)Ga_(0.845)As 3.5053 2.50 GaAs_(0.90)P_(0.10) 3.4607 1 68.00GaAs_(0.90)P_(0.10) 3.4607 5 2.50 GaAs_(0.90)P_(0.10) 3.4607 8.00In_(0.155)Ga_(0.845)As 3.5053 2.50 GaAs_(0.90)P_(0.10) 3.4607 1 34.00GaAs_(0.90)P_(0.10) 3.4607 1 76.00 GaAs_(0.56)P_(0.44) 3.3248 23 83.01AlAs 2.9459 71.14 Al_(0.12)Ga_(0.88)As 3.4345 1 83.01 AlAs 2.9459 1142.00 Al_(0.12)Ga_(0.88)As 3.4345 10 67.21 AlAs 3.0054 56.60Al_(0.12)Ga_(0.88)As 3.5682 1 120.00 GaAs 3.5110

An implementation, such as that shown in Table 1, is just one of manypossibilities and would be grown as a bottom emitter (upside down) sothat the entire GaAs substrate could be removed to enable more efficientcooling of the mounted semiconductor chip. This removal would expose theIn_(0.49)Ga_(0.51)P 155.40 nm cap layer to air. Additionally this caplayer could be AR-coated as shown in the arrangements of FIGS. 1, 3, 4A,8, 17, 19, 21, 23 and 25. This is one of many arrangement options for abarrier pumped setup at 808 nm and a laser signal at 980 nm. Itcorresponds to one possible realization of the 5:5 MQW structure shownin FIG. 17 below.

In addition to a reflecting DBR for the signal wavelength at 980 nm (23repeats in the example of Table 1), it also has a pump-light reflectingDBR at 808 nm (10 repeats), allowing for multiple passes of the pumpbeam. (A similar DBR has already been implemented for a variant on anRPG structure, called a MIXSEL by B. Rudin, V. J. Wittwer, D. J. H. C.Maas, M. Hoffmann, O. D. Sieber, Y. Barbarin, M. Golling, T. Sudmeyer,and U. Keller, High-power MIXSEL: an integrated ultrafast semiconductorlaser with 6.4 W average power, Opt. Exp., 18, 27582, (2010),incorporated herein by reference in its entirety.)

In one implementation, a superlattice structure can be configured as avariant by thinning the QWs and barriers further. For example, asuperlattice structure is formed by 3.4 nm QWs and 1.7 nm barriers withelectron and hole wavefunctions delocalized across the structure. Otherconfigurations of conventional (and possibly superlattice) structuresutilizing barrier, in-well or electrical pumping are within the scope ofthe invention and target different pump wavelengths (optical pumping)and emission wavelengths and optionally are based on different materialcompositions, thicknesses and material types. One of ordinary skill inthe art will understand that similar structures can be implemented atother pump wavelengths and center laser wavelengths.

Example I

FIG. 3 provides a schematic illustration of a related implementation ofthe laser gain medium according to the idea of the invention. Onesignificant feature of this specific implementation is that more thanthree (as shown—ten) QWs 302 are packed in a single MQW unit, formingthe cumulative MQW structure of the invention, with sub-wavelengthspacing d and under only one half-cycle 304 of a single standing wavethat is formed in operation of the structured in a laser cavity.Generally, however, sub-wavelength spaced densely packed quantum wellscan be packed within an extended structure covering multiple fieldperiods (as is further discussed below). The fundamental physics ofmode-locked behavior is now fundamentally changed from that representingthe mode-locking operation of the conventional lasers. Using anembodiment of the cumulative MQW structure configured according to anidea of the invention, there is an emergence of full nonequilibrium,nonlinear dynamics, where the interacting electron/hole subsystemswithin their respective bands act in concert to effectively sweep outmost of or possibly the entire carrier inversion and generate an optimalultrashort mode-locked pulse train. In this disclosure, a basicstructure illustrated in FIG. 3 (namely, a MQW unit containing at leastthree QWs and located between the immediately neighboring nodes 310, 312of a standing wave formed along an optical axis in the semiconductorgain medium during the lasing operation) is used as the base unit cellthat can be replicated multiple times to produce an extended cumulativeMQW structure of the invention.

Example II

FIG. 4A shows a schematic of one implementation of the cumulative MQWstructure for a mode-locking laser of the invention. Here, line 4A.3shows a standing wave pattern at a first wavelength (such as the centerwavelength corresponding to the central carrier frequency of theresulting pulse), while lines 4A.1 and 4A.2 show standing wave patternscorresponding respectively to a short wavelength and a long wavelengthof the full gain spectrum indicated by the arrows in FIG. 4B at 1.35 eVand 1.15 eV respectively.

FIG. 4A depicts a single half-wavelength structure with ten (10) QWs 404packed at sub-wavelength spacing across a region occupied by singlehalf-wavelength cycle of the standing wave formed during the lasingoperation. In addition to the single standing wave at the central pulsewavelength (line 4A.3), standing wave fields corresponding to thosewavelengths (frequencies) at the short (line 4A.1) and long (line 4A.2)wavelength extremes of the full linear gain spectrum shown by line 4B.1in FIG. 4B are also included. These latter standing waves are very muchsmaller in amplitude but are artificially enhanced in amplitude forclarity of presentation. The arrow 410 to the right in FIG. 4B extendsjust beyond the end of the linear gain spectrum (line 4B.1) indicatingthat the generated pulse has nonlinearly excited energy outside of thislinear gain spectral window. Considering the time-bandwidth product oftransform limited pulses, the ability to arrange QW stacks within cacumulative MQW structure to extract photons across the full spectralwidth enables an MQW-based laser system of the invention to generatepulses with the shortest possible duration. By tightly packing thin QWswith very thin barriers (as shown, for example, in FIG. 4A) the goal ofbeing able to convert all or most of the available carriers in theconduction/valence bands of the semiconductor active structure intolight is achieved.

FIG. 4B provides a plot of the full linear gain spectrum (line 4B.1),the absorption of the single QW saturable absorber (line 4B.2), the netgain (difference between the lines 4B.1 and 4B.2) shown as line 4B.4and, the dashed upper curve showing the spectrum of a mode-locked pulseproduced by the arrangement in FIG. 4A (line 4B.3). In starkcontradistinction with the net gain approach based on which lasers ofthe related art are defined, it was observed that the spectrumrepresented by line 4B.3 is so broad that it closely matches the fulllinear gain spectrum (line 4B.1) and produces a dramatically shorterduration pulse than would be expected from considering only net gain ofline 4B.4. It is noted that even the solution described in FIGS. 4A, 4Bis not necessarily optimal. In fact, the linear gain concept shown inFIGS. 4A and 4B provides only an initial cumulative MQW structure, whichis further optimized, according to the idea of the invention, with theuse of full nonlinear optimization on the running mode-locked laser.

The cumulative MQW structure of FIG. 4A contains only one, single MQWunit 406, and can further be used as a building block for relatedimplementations of cumulative MQW structures of the invention byextending the concept to multiple half-wavelength repeats of the MQWunit 406 throughout the length of the gain medium, although care must beexercised in placement of the QWs downstream in a multi-repeatstructure. The reason for this is that the standing wave fields arelocked in place at the DBR-active region boundary and they rapidly runout of phase as one moves further to the right. Multiple repeatstructures beyond that described in the present document may requiredifferent strategies for placement of QWs.

Example III is discussed in reference to FIGS. 1, 3, 5A, and 5B. FIG. 5Aillustrates the linear gain (line 5A.1), SESAM absorption (5.A.3) andnet gain (line 5A.2) for a conventional RPG structure (such as that ofFIG. 1). In comparison, FIG. 5B illustrates the calculated linear gain(line 5B-1), SESAM absorption (line 5B-2) and net gain (line 5B-3) forthe cumulative MQW structure of the embodiment of FIG. 3. It is readilyapparent that the conventional RPG structure has a significantly largernet gain than the cumulative MQW structure of the invention, and the theRPG gain bandwidth is likewise narrower than that of the cumulative MQWstructure. Based on this traditional linear net gain picture, the RPGdemonstrates pulses that, while growing faster from noise, end up withbroader time duration that those produced by a cumulative MQW structureof FIG. 3, due to the narrower gain bandwidth.

It should be noted that, while the presence of optical elements (such asquantum well, graphene, carbon nanotube saturable absorbers or eventransparent Kerr Lens based mode-locking elements) in the optical cavitymay facilitate the mode-locking operation of an embodiment o theinvention, such presence is not necessarily required, and in someimplementations a system of the invention may be configured to operatein a self-mode-locking regime.

The basic principle of mode-locking with a saturable absorber wasdiscussed in H. A. Haus, “Theory of Mode Locking with a Slow SaturableAbsorber,” IEEE J. Quantum Electron. 11, pp. 736-746 (1975),incorporated herein by reference in its entirety, and in H. A. Haus,“Mode Locking of Lasers,” IEEE J. Sel. Top. In Quant. Electron., 6, 1173(2000), each of which disclosures are incorporated herein by referencein its entirety. The idea is that the combination of gain, over a broadrange of frequencies (wavelengths), and saturable absorption results ina net gain (gain minus absorption) as shown in FIG. 4B as an example.The net gain is depicted by the narrow window indicated by the two solidblack arrows pointing down in that figure and is plotted as the curve(line 4B.4) at the base of this figure. This net gain window is muchnarrower than the total gain spectrum indicated by the solid (line 4B.1)curve on the same figure. Based on the net gain window, one would expectthe pulse duration to be relatively long due to the narrow frequencyband available for amplification of light. However, contrary toconventional expectations, the net gain window does not adequatelypredict the behavior of the novel MQW structure. I. Kilen, J. Hader, J.V Moloney, and S. W. Koch (in Ultrafast Nonequilibrium Carrier Dynamicsin Semiconductor Laser Mode-Locking, Optica, 2014) show that instead ofthe net gain, one has to refer to the spectral width of the carrierinversion to predict the correct behavior of novel MQW modelockingstructures. The linear gain model concept has been employed in modelinga broad class of solid state mode-locked laser systems and applied toVECSELs recently by O. D. Sieber, M. Hoffmann, V. I. Wittwer, M.Mangold, M. Golling, B. W. Tillma, T. Sudmeyer and U. Keller,Experimentally verified pulse formation model for high-power femtosecondVECSELs, Appl. Phys. B. 113, 133 (2013), incorporated herein byreference in its entirety.

Example IV

FIG. 6 provides modeling results of comparison among severalconventional RPG structures (one containing 6 individual QWs, each at acorresponding node of the standing wave; another containing similarlypositioned 8 QWs; and yet another having 10 QWs to it) and severalembodiments of a cumulative MQW structure of the invention (configuredaccording to the principle of FIG. 3 but containing 6, 8, and 10 QWs,respectively) are provided in FIG. 6. In each of the consideredcumulative MQW structures, respectively corresponding 6, 8, and 10 QWsare packed around a single anti-node of the standing wave field, underone cycle of the standing wave.

FIG. 6 indeed confirms that peak pulse amplitudes for each of the 6, 8and 10 QW structures in the RPG initially grow more rapidly than theircumulative-MQW counterparts. Later in the dynamical evolution it isobserved that a dramatic switch occurs in growth rate of the pulsepeaks. The peak pulse amplitude for each of the MQW structures sweepspast the RPG counterparts and saturates at peak amplitudes that are afactor of approximately 2.5 larger. Stated differently, the peakintensities become about 6 times larger. Not shown in FIG. 6 are thecorresponding pulse durations. However, all the RPG pulses aresignificantly longer than 100 fs, whereas the pulses produce by any ofthe assessed cumulative MQW structures are sub 100 fs in duration.

Example V

It was also demonstrated that a further dramatic difference in dynamicalbehavior occurs by contrasting robustness of lasing operation of a lasersystem that contains a cumulative MQW structure of the invention overthat containing a conventional RPG structure. The comparison takes twonominally identical (with the same starting inversion in each well)structures that initially demonstrate a comparable net positive gain.These structures are the one shown in FIG. 7 (i.e., an RPG structurewith 10 QWs) and the one shown in FIG. 8 (i.e., a cumulative MQWstructure containing a single MQW unit 804 with ten QWs; unit 804 spacedacross a distance exceeding the axial extent of a single cycle of thestanding wave representing intensity of the field formed during thelaser operation along the gain medium). Once mode-locking operation isestablished, the inversion is systematically reduced below the zero netgain limit.

FIG. 9 displays the initial time development towards a stablemode-locked state for the RPG structure of FIG. 7 (lower peaked lineRPG: 2.10) corresponding to an initial carrier density of 2.10×10¹⁶ m⁻²,and that for the cumulative MQW structure of FIG. 8 (higher peaked lineMQW: 3.86), corresponding to an initial carrier density of 3.86×10¹⁶m⁻². Once the stable mode-locked state has been reached and themode-locking operation is established, the initial inversion for eachstructure is systematically decremented initially towards a net gain ofzero (line RPG-2.00) for the RPG and (line MQW-3.65) for the MQW,corresponding respectively to a carrier density of 2.00×10¹⁶ cm⁻²and3.65×10¹⁶ m⁻² for the RPG and MQW structures, respectively. Followingthis, the inversion is decremented further entering the net absorptionregion until such a point that the mode-locking is lost and the systemreturns to the CW lasing state. The operation of the RPG structureimmediately returns to the CW state below zero net gain. The sets ofcurves for the cumulative MQW structure on the right show thatmode-locking is sustained well into the net linear absorption region(see FIG. 11). In FIGS. 9, 10, and 11, each curve associated with a gainlevel is labeled accordingly, and these curves illustrate the gain andenergy extraction dynamics with respect to the carrier density beingdecremented.

From the results of FIG. 9, a dramatic difference in the dynamicalevolution of each of the mode-locked systems of FIG. 7 (conventionalRPG) and FIG. 8 (an embodiment of the cumulative MQW of the invention)is verified, as one moves into a net absorption limit. Indeed, the RPGstructure remains mode-locked at zero net gain but then switches back toCW operation below this point. In stark contrast, the much higher peakamplitude and shorter duration of pulses produced by the mode-lockedcumulative MQW structure remain mode-locked well into the net absorptionregion, thereby displaying a strong and robust hysteresis behavior. Thecumulative MQW structure is a truly nonequilibrium nonlinear dynamicalsystem that remains in its mode-locked state even though the systemexhibits a strong net linear absorption. While hysteresis might beobserved in mode-locked lasers in general, those hysteresis phenomenaare the result of residual thermal effects in contrast to the situationobserved here where such long term thermal effects are not consideredand the hysteresis is intrinsic due to many-body effects.

FIG. 10 and FIG. 11 contrasts the RPG and cumulative MQW structures thedynamics of which are shown in FIG. 9. FIG. 10 shows the linear gain fordecreasing carrier densities (line Gain: 2.10, line Gain: 2.00, lineGain: 1.94) of the RPG structure for the densities whose dynamics areshown in FIG. 9 and displayed on the curves. The black curve (line Abs)is the fixed SESAM absorption for each case. FIG. 11 shows the lineargain versus carrier density for the cumulative MQW structure of FIG. 8the dynamics of which are displayed in FIG. 9. Usually the difference ofthe gain and absorption defines the net gain, although here a netabsorption is obtained when the peak gain lies below the absorption.

FIG. 10 and FIG. 11 plot the linear gain and SESAM absorption for thedifferent carrier densities used in FIG. 9. When the linear gain exceedsthe SESAM absorption, the difference yields the net linear gain. Afinite net linear gain is necessary to cause the buildup of theintra-cavity field and establishment of mode-locked behavior. It isnoted that the RPG mode-locking survives even when the net gain is zero(peak gain=absorption in the left figure) but the mode-locking reversesto a CW state for any finite net absorption (peak gain<absorption). Onthe other hand, the cumulative MQW structure is remarkably robust andremains mode-locked even for large linear net absorption leading to ahysteresis cycle in pump power.

This dramatic enhancement of peak intensities of laser output obtainedwith the use of the cumulative MQW structure based architecture isexplained by better extraction of carriers from the entire inversionspectrum. This can be understood in terms of the nonequilibrium electronand hole carrier density dynamics, or in this context, nonequilibriuminversion (n_(e)+n_(h)−1), where n_(e),n_(h) are the electron and holecarrier densities respectively. Initially in the dynamical evolution,each QW in the subwavelength stack of the cumulative structure of FIG. 8acts independently and those close to the maximum of the field (at theantinode) grow fastest although slower than the RPG structure of FIG. 7,which also has 10 such QWs seeing an identical peak gain. However, whilethe RPG structure is restricted to drawing carriers from the same rathernarrow spectral window centered about its central pulse frequency, thesubwavelength spaced QWs in the cumulative MQW structure act together soas to efficiently sweep out a much broader swath of carriers (in somecases almost all) and convert them into a giant sub 100 fs pulse. Whenoptimized, the QW sub-wavelength spacing or QW composition can beadjusted to sweep out most of the inversion leading to the shortestpossible duration fs pulse train.

Example VI

It has been established numerically that the use of a cumulative MQWstructure in a laser system of the invention delivers much higher pulsepeak powers than the use of an RPG structure as illustrated in FIG. 9,which is not obvious at all from the FIG. 9 plots.

To this end, FIG. 14 shows that the performance of the cumulative MQWstructure is much better than that of the RPG structure from the pointof view of delivering pulses of substantially higher energy. This casecorresponds to the inversion being just above threshold for lasing sothat the energies represent the lowest achievable. If pumped at a higherlevel, however, the difference in energy output becomes even larger.

Further to this end, FIG. 15 shows mode-locked pulse peak powers for thelaser systems including, respectively, cumulative MQW structuresdiscussed in reference to FIG. 6 (with 10, 8 and 6 QWs packed at asingle anti-node of the standing wave field). FIG. 16 shows thecorresponding energy fluencies for a 500 μm spot of the pump radiationon the laser chip containing such cumulative MQW structures. FIG. 15 andFIG. 16 confirms the observations about advantageously higher poweroutput from the cumulative MQW structure as the pulse energies reach0.25 nJ for the 10 MQW structure. Here 6-, 8- and 10-MQW structures arecompared and show the time evolution towards fixed mode-locked peakamplitudes on the left and the corresponding pulse energies on theright.

Example VII

As shown in FIG. 21, a related implementation of the cumulative MQWstructure of the invention includes an 8:8 MQW structure 2102, whichcontains two MQW units (or base cells) 2104, 2106. Each of the units2104, 2106 includes 8 QWs packed within a respectively-correspondingcycle of axial field intensity distribution shown as 2110. Theimmediately neighboring nodes 2112A, 2112B of the intensity distribution2110 are located on the opposite sides of the MQW unit 2104, while theimmediately neighboring nodes 2112B, 2112C are located on the oppositesides of the MQW unit 2016. FIG. 22 shows the mode-locked pulse formedwith the use of the cumulative MQW structure 2102, with a pulse durationof 43.1 fs and a quadratic chirp.

FIG. 12 and FIG. 13 contrast the inversion dynamics of the conventionalRPG and the cumulative MQW structures. FIG. 12 shows snapshots of theinversion depletion for the RPG structure as the pulse sweeps throughthe gain chip. FIG. 13 shows snapshots of the inversion depletion forthe 8:8 MQW structure 2102. The carrier depletion of the RPG structureleaves much more unsaturated (unused) carriers after the pulse hasexited the gain chip. On the other hand, the cumulative MQW structure2102 is depleting carriers across the entire spectral range (line 13.1).This yields a mode-locked pulse duration of approximately 43 fs with arelatively small chirp. Such very short pulse duration supports theconjecture that the shortest pulse possible can be generated if theplacement of the QWs could be arranged to sweep out the entireinversion. Line 13.1 in FIG. 13 shows that the inversion is indeeddepleted over a wide spectral range. Note that there is still unusedinversion in the wings of line 13.1 for this case. Possible optimizationof structure 2102 may include optimization of the QW spacing and wellcompositions, for example, such that there is no inversion left in thesystem after the pulse has passed. This would produce the shortestpossible duration pulse which should be resilient against pulse breakupas there are no further unsaturated carriers available to produceamplication.

Example VIII

FIG. 17 shows another implementation of the idea of the invention,according to which the cumulative MQW structure 1704 contains two MQWunits 1706, 1708, each of which packs five 5 QWs around each of the twoadjacent field anti-nodes such that the immediately neighboring nodes1712A, 1712B of the standing wave 1716 (formed during lasing along theoptical axis of the structure 1704) are located on the opposite sides ofthe MQW unit 1706, while the immediately neighboring nodes 1712B, 1712Care located at the opposite sides of the MQW unit 1706.

The MQW arrangement 1704 utilizes the replication of a base MQW unitwith 5 QWs to produce a 5:5 structure. FIG. 18 shows the calculatedmode-locked pulse of duration 86.1 fs resulting from the operation ofsuch 5:5 structure in a laser system, and the phase of the pulse, whichexhibits a small amount of chirp. Generally, when the residual chirpremains in operation, dispersion compensating elements can be introducedwithin or external to this or any other implementation so as to reducethe chirp (flatten the phase) and further reduce the pulse timeduration. (For example, for use with a standard laser a chirped mirrorcan be designed to compensate for chirp in the pulse; in mode-lockedfiber lasers a section of fiber can be made of a dispersive material tocompensate for other dispersion, or an optical compensator can beemployed to compensate for linear chirp.)

Example IX

One of the advantageous features of the proposed cumulative MQWarrangement over the systems of related art is that packing of theconstituent QWs is very flexible. For example, as shown in FIG. 19, a5:5 arrangement of the MQW structure of FIG. 17 is complemented withadditional QWs 1902, 1904, and 1906 outside and in-between the MQW units1706, 1708. The resulting structure has total of six additional QWs. Inthis implementation, the 5:5 MQW structure of FIG. 17 is extended byfilling the space (within each standing-wave antinode, that has not beenalready occupied by QWs) with additional QWs to effectively increase thenumber of total QWs within each occupied antinode to eight. FIG. 20shows the resulting mode-locked pulse of duration 83 fs and the phaseacross the pulse. A comparison of the results of FIG. 20 with those ofFIG. 18 reveals that the pulse shape and phase are very similar betweenthese two similar configurations of the cumulative MQW structures.

Example X

In a related embodiment, by arranging the QWs to lase at longerwavelength, even more QWs can be accommodated within a single half-cycleof a standing wave field.

In one implementation, shown in FIG. 23, a ten-QW cumulative MQWstructure 2304, configured to operate at 1200 nm, is shown. FIG. 24presents plots showing mode-locked pulses of 84 fs duration, supportedby such structure during the lasing operation.

Example XI

In one implementation, FIG. 25 shows a sixty-QW MQW structure 2504,which includes six MQW units each containing 10 QWs per fieldhalf-cycle. Notably, the six MQW units are located sequentially tocoincide with sequentially-defined field half-cycles such that each ofthe nodes 2512A, 2512B, 2512C, 2512D, 2512E (of the field's standingwave distribution) that is intermediate to the MQW units is formedbetween the two immediately neighboring MQW units. The gain medium ofthe laser system of this embodiment is configured such that the nodes2514, 2516 that are the outer nodes in the sequence of immediatelyneighboring nodes (2514, 2512A, 2512B, 2512C, 2512D, 2512E, 2516) arelocated on the opposite sides of the cumulative MQW structure 2504.

Notably, there is a possibility that the use of this structure 2504 mayresult in generation of a wider pulse, due to the strong interference ofwaves to the right of the structure 2504 due to an accumulating phasedifference. As followed from the numerical analysis presented in FIG.26, a corresponding mode-locked pulse had a duration of 205 fs. It canbe concluded that this multiple repeat MQW structure is not optimized toproduce the shortest possible pulse—a full nonlinear optimizationconfigured according to the idea of the invention is required to achievethis goal. However, this example illustrates the breadth of the generaldesign principles.

Additional Examples

The residual carriers remaining on the low and high momentum (frequency)end of the inversion on the right in FIG. 13 (line 13.1) indicate thateven shorter pulses can be generated if the MQW can be arranged to sweepout these excess carriers. Each QW can effectively have carriers acrossthe full spectral window depleted by using optimum positioning andspacing of the QW stack within the structure. This optimum positioningand spacing of the QW stack within the structure corresponds with theQWs being packed sufficiently close so as to have each individual QWdepleting carriers across the full available spectral window, which isachieved by using thin QWs (less than 8 nm) with narrow barriers (lessthan 10 nm spacing). The final grown structure could also be asemiconductor superlattice where carriers are shared amongst QWsalthough for the spacings shown below, the lowest subband in each QW iseffectively unperturbed by its neighbor.

FIGS. 27-34 show simulations investigating two situations where thefinal outcome is essentially the same although the initialization of themode-locking is very different. FIG. 27 shows a schematic of a 10 QW MQWstructure with QW thicknesses and spacing reduced so as to accommodatemore spectral bandwidth for more effective depletion of carriers. FIG.28 shows a linear gain spectrum for high inversion (line 28.1) withinitial carrier density of 5.0×10¹⁶ m⁻² and high SESAM absorption (line28.2) as well as the net linear gain (line 28.3). FIG. 29 shows amode-locked 23.8 fs pulse amplitude showing weak chirp (phase) acrossthe pulse. FIG. 30 shows the final pulse spectrum in its finalmode-locked form. It can be seen that the pulse spectrum extends beyondthe linear net gain bandwidth shown by line 28.3 in FIG. 28 andindicated as the shaded region here.

Similar to FIGS. 27-30, FIG. 31 shows a schematic of the identical 10 QWMQW structure as shown in FIG. 27 with QW thicknesses and spacingreduced so as to accommodate more spectral bandwidth for more effectivedepletion of carriers. FIG. 32 shows a linear gain spectrum for lowerinversion (line 32.1) with initial carrier density of 3.0×10¹⁶ m⁻² andhigh SESAM absorption (line 32.2) as well as the net linear gain (line32.3). FIG. 33 shows a mode-locked 32.4 fs pulse amplitude showing analmost flat phase across the pulse. The resulting pulse is close tobandwidth limited. FIG. 34 shows the pulse spectrum of the finalmode-locked pulse shown in FIG. 33. A key difference between thesimulation shown in FIGS. 27-30 and the simulation shown in FIGS. 31-34is that the inversion (pumping) is reduced so as to just exceed the gain(compare line 28.3 in FIG. 28 and line 32.3 in FIG. 32). FIG. 34 showsthat the final broadened spectrum greatly exceeds the narrow initial netgain (shown in FIG. 34). The initial net gain bandwidth bears littlerelationship to the actual broadened spectrum of the 32.4 fs pulse shownin FIGS. 33 and 34.

In each of the two simulations shown in FIGS. 27-34 pulses are generatedwith mode-locked pulse durations of approximately 24-30 fs, each pulsehaving a slight correctable or almost nonexistent linear chirp. The netgain picture becomes meaningless and it is noted that the pulse spectrumapproaches the full gain bandwidth limit irrespective of the SESAMabsorption or cavity outcoupling loss. FIGS. 27-30 provide a dramaticillustration of this statement where conditions for both simulations areidentical except for the initial inversion in the QWs of the MQWstructure. In FIGS. 27-30 the inversion is 5*10 m⁻², whereas in FIGS.31-34 the inversion is set to 3*10⁻¹⁶ m⁻². In the first case,corresponding to strong pumping the gain considerably exceeds the SESAMloss leading to a large and spectrally broad net gain in the system. Thefinal mode-locked pulse has a spectral bandwidth that still exceeds thenet linear gain bandwidth as seen earlier although not by a lot. InFIGS. 31-34, the reduced gain leads to a much smaller difference betweengain and SESAM absorption resulting in a smaller and much narrowerlinear net gain spectral bandwidth (line 32.3).

However, the final mode-locked pulse spectrum expands way beyond thelimited net gain bandwidth (shaded region in FIG. 34) and almost coversthe entire linear gain spectrum. This result emphasizes that this formof mode-locking is truly nonequilibrium by nature and cannot be guidedby the usual net gain bandwidth argument. A key observation in FIGS.31-34 is that the 32.4 fs pulse spectrum FIG. 33 replicates the shape ofthe full linear gain spectrum (line 32.1 in FIG. 32) indicating thatalmost all available carriers are being used independently of SESAM andoutcoupling mirror losses (see example below in FIGS. 35-36). This isthe case being illustrated in FIGS. 4A and 4B above. Also in this weaklynonlinear operating regime, the phase across the pulse in FIG. 33 isalmost flat indicating essentially no chirp and a close to bandwidthlimited pulse. In FIGS. 27-30, at much higher initial inversion (andlinear gain relative to a fixed absorption), the pulse spectrum likewiseextends across the full accessible gain bandwidth but is now stronglydistorted.

Practical Implementation of Specific Lasing Structures, Solutions forGrowth-Caused Dislocations, and Gain Increase

While the change of a conventional RPG-based gain structure to ajudiciously configured MQW-based gain structure, discussed above, allowsthe user to overcome the problem of strong chirping of pulses and todrive a nonlinear phase transition to engage most of the carriersdefined within the full gain spectrum so as to repeatably achieve thesought-after ultra-short pulse operation of the resulting VECSEL, the“spreading apart” of individual constituent QWs of a given MQW uniteffectively amounts to offset of at least some of such constituent QWswith respect to a peak of the gain curve form the given MQW unit and,therefore, to a reduction of gain available for operation of such MQWunit.

At the same time, it has been empirically discovered that, during theprocess of growth of the cumulative MQW structure of embodiments of theinvention under certain conditions, excess strain and/or stress is beingbuilt into the structure being formed, causing the origination ofdefects, in the resulting laser structure, which acted as sites wherethe excited carriers (the electron-hole pairs in the gain medium)recombine non-radiatively. This, in practice, led to reduction or evenabsence of lasing. Alternatively or in addition, such non-radiativerecombination also led to very strong heat generation with a potentialdetrimental outcome of local damage to the resulting semiconductorstructure and/or prevention of lasing operation in a desired short-pulseregime.

These two shortcomings—the potential reduction of gain and the formationof dislocation upon growth—appear to accompany the above-discussedsolution for shortening the duration of pulses during the mode-lockedoperation of the VECSEL structure, and may require separate attention.One aspect of the following investigation begs a question of determininga fashion of optimization of the gain structure such as to reduce—oreven prevent—the formation of dislocations upon growing the gainstructure, while another addresses the issue of whether it is possibleto compensate the observed gain reduction in some shape or form, bothwithout sacrificing the advantages provided by the MQW-based embodimentsover those based on the RPG.

The example of the observed stress/strain problems is now illustrated toFIGS. 48, 49, 50, 51A and 51B.

The schematic of a cross-section of am MQW structure denoted as “MQW44”,which had two MQW units 4810A, 4810B each containing foursubstantially-equidistantly spaced from one another QWs 4814 (and, inpractice, each located between two immediately-neighboring nodes of thestanding optical wave 4820 formed in the laser cavity utilizing theMQW44 structure), is shown in FIG. 48. FIG. 49 illustrates a simulatedlaser-pulse output from a 2×4 VECSEL, built with the use of the MQW44structure in a linear cavity with SESAM and the output coupler, boastinga FWHM pulse width of about 74 fs. The attempt to grow the MQW44structure (or similar structures) with the InGaAs/GaAsP material systemthe analysis of which suggested that, in practice, the devices possessedsubstantial structural material (accumulated) strain, as illustrated inplots of FIG. 50. The presence of accumulated strain/stress was deducedfrom the extension of at least some of the plots A, B, C outside of theband or area within the +/−20% lines 5010A, 5010B (which are empiricallyconsidered in the art to indicate the dislocation-free growth of asemiconductor structure) and suggested the presence of built-updislocations. A dislocation is known to be a crystallographic defect, orirregularity, within a crystal structure, strongly influencing theproperties of materials. (Some types of dislocations are oftenvisualized as being caused by the termination of a plane of atoms in themiddle of a crystal. In such a case, the surrounding planes are notstraight, but instead they bend around the edge of the terminating planeso that the crystal structure is perfectly ordered on either side.)Image of photoluminescence (PL), produced with such grown structure andillustrated in FIG. 51A, confirmed the empirical findings ofdislocations by showing very pronounced dark-line defects 5110,extending as shown vertically and horizontally across the distribution5120 of light in the image. (In FIG. 51B, which is provided forillustration purposes only, the location of dislocations across theimage of FIG. 51B is traced and the dislocations are emphasized andenhanced, for better visibility, with lights 5110A). As shown, theilluminated spot 5120 is on the order of 400 micron FWHM diameter (whichis a typical size of a spot of pump-light beam used to pump the VECSELstructures to obtain lasing)

Further embodiments of the invention address this practical problem thatmay arise during the implementation of growth of the discussedjudicially-configured MQW structure(s) and that manifests, under certaincircumstances, in excessive formation of dislocations that substantiallyreduce (if not completely negate) the efficiency of practical lasing ofa given laser utilizing so-configured MQW structures. As alreadymentioned, the implications of excessive dislocations caused by growthof a semiconductor structure containing MQW unit(s) of the invention,include excessive tensile stress or strain and/or compressive stresswhich, accumulated or built up throughout the gain medium containing MQWunit(s) of the invention, forms defect site(s) where the excitedcarriers recombine non-radiatively and, therefore, do not contribute tothe light amplification process. According to the idea of the invention,such practical problem is solved by structuring or configuring at leastone of the MQW units of the invention to contain constituent (at leastthree per MQW unit) QWs that are intentionally spaced non-equidistantlyfrom one another, as measured along the axis of the gain medium. Theemployed “non-equidistant” QW-positioning within a given MQW unit can beemployed regardless of an overall structure of the gain medium (forexample, regardless of and with no connection to a particular number ofthe MQW units present in the gain medium of a particular VECSEL chip,and/or regardless of and with no connection to a particular structure ofthe optical window of the VECSEL chip, and/or regardless of and with noconnection to how QWs of a given MQW unit may be offset with respect tothe node/antinode of the standing wave pattern formed, during theoperation along the gain medium chip), as discussed in more detailbelow.

The proposed practical solution to such strain problem plaguing theprocess of growth of the MQW structure ensures that the light outputfrom a VECSEL structure utilizing the grown MQW structure is stillrealizable in a form of ultrashort pulse generation. One embodiment ofthe solution was rooted in a judicious modification of the the gain partof the VECSEL chip. The solution is characterized by a combination ofthe following general features: (i) a sufficiently high number ofindividual QWs of a given MQW unit disposed close to the antinodes ofthe electrical field distribution (formed along the VECSEL cavity) inorder to provide enough gain, while, at the same time, (ii) havingindividual QWs of the given MQW unit somewhat removed from the antinodeposition to provide gain for the broad band of different spectralfrequencies that are available to support the shortest physicallyrealizable pulse, and (iii) within a given MQW unit, avoiding havingmore than two QWs sufficiently close to one another in order to preventexcessive strain build-up.

The proposed practical solution to the “reduction of gain”, caused bythe use of MQWs instead of the conventional RPG, is turning on the ideaof maximizing the gain so as to boost the average and peak power of thegenerated ultrashort mode-locked pulses. The gain can be boosted backclose to the level(s) provided by the original RPG-based structure byadding a single, stand alone QW near the DBR mirror. The use of such“gain-booster” QW was unexpectedly found to offset other competinglosses (such as outcoupler losses and SESAM saturable losses) within theVECSEL cavity. It is appreciated that the solution to the strain problemand the gain-boosting solution can, in practice, to be used eitherindependently from one another or simultaneously, as the followingdiscussion indicates.

Example XII

One implementation, referred to herein as “121-121” or “2×121” forsimplicity, has 8 (eight) QWs organized in two MQW units 5210A, 5210B,as shown schematically in FIG. 52. In each of these 4-QW MQW units5210A, 5210B, the two peripheral QWs (marked as A and D) at the wings ofthe corresponding MQW unit are spaced from the immediately neighboringQW of the unit by spacing(s)/barrier layers that are different from the(spacing/barrier layer) separating the two centrally-located QWs B andC: d₁≠d₂, d₃≠d₂. In other words, the constituent QWs of a given MQW unitare spaced non-equidistantly with respect to one another.

The term “non-equidistant spacing” or a similar term, unless definedotherwise, is generally intended to denote and refer to the situationwhen the barrier layers or barriers separating neighboring constituentQWs of a given MQW unit have unequal thicknesses (in this specific case,thicknesses d₁, d₂, d₃ related to one another as d₁≠d₂, d₃≠d₂).

It was empirically found that, in one specific case, in a MQW of the“121-121” type structure the barrier spacing d₂ between the middle QWsB, C could be on the order of one QW thickness (with a thickness of atypical QW between about 8 nm and about 12 nm). The barrier spacing(s)d₁, d₃, on the other hand, could be sufficiently large to avoidpromoting dislocations due to strain, for example on the order of 2× to10× an individual QW thickness. Generally, the spacing(s) need(s) to beoptimized to accommodate a combination of competing processes: 1) topromote amplification of as broad a span of possible of wavelengthsabout the central wavelength so as to produce the shortest possible timeduration pulse (moving the QWs away from the field anti-node reduces thegain) and 2) to retain enough gain across this broad band of wavelengthsso as to overcome all losses in the cavity. The latter include saturableand unsaturable losses in the SESAM and various unsaturable lossesincluding output coupling losses, or example. The example of the“121-121” gain structure provides a reduction to formation ofdislocations upon gain-structure growth.

FIG. 53 shows a simulated output pulse produced by the chip utilizingthe MQW structure of FIG. 52 in a linear cavity with SESAM and outputcoupler.

Example XIII

A related implementation, referred to as “1-121-121” or “1+2×121” designand shown in FIG. 54. Here, the structure 5400 includes 9 individual QWseight of which are organized into 2 MQW units 5410A, 5410B (eachcontaining 4 individual QWs A, B, C, D, by analogy with the structure ofFIG. 52) and an additional, auxiliary QW E of which is inserted close tothe DBR (not shown) of the VECSEL structure) in order to improve thegain of the chip without sacrificing the short-pulse generation. Thestand-alone QW E is a gain-boosting QW. This implementation (and otherimplementations structurally similar to this one) provide an answer tosimultaneous reduction of growth-related dislocations and increase ofgain available to the carriers. Notably, and according to the idea ofthe invention, the overall VECSEL structure is configured such that eachof the MQW units 5410A, 5410B is located, in practice, between theimmediately neighboring nodes (5420A, 5420B) and (5420B, 5420C) of thestanding electrical field 5430 formed along the VECSEL structure.Notably, and according to the idea of the invention, in each of the MQWsunits 5410A, 5410B of the “1-121-121” design the individual QWs A, B, C,and D are spaced non-equidistantly. FIG. 55 shows a simulated outputpulse of the chip utilizing the MQW structure of FIG. 54 in a linearcavity with SESAM and output coupler

FIG. 56 illustrates the plots of accumulated strain for the newlydesigned VECSEL chip with the “121-121” arrangement of the individualQWs (line II) and the “1-121-121” arrangement (line I). As determined,the integrated strain shown by lines I, II remains well within theregion of +/−20%, which corresponds to growth without excessiveformation of dislocations. An image 5700 (of FIG. 57), produced with theuse of photoluminescence captured from MQW “1-121-121” containing chip,showed the absence of dark line dislocations. The illuminated spot wason the order of 400 μm, which was a typical pump spot size.

In order to yet further increase the net roundtrip gain, the structuressimilar to those of FIGS. 52, 54 were also implemented with theincreased number of repeats of the “121” MQW-unit arrangements (such as,for example, a structure containing 3 corresponding “121” MQW units—a“3×121+1” structure; or a structure containing four (4) corresponding“121” MQW units—a “4×121+1” structure; and so on). In each of suchdesigns, containing at least two MQWs with non-equidistantly spacedindividual QWs the image of PL evidenced substantial lack of growthdislocations that was attributed to intentionally-non-equidistantcoordination among the individual QWs of such MQW units. Some of suchauxiliary implementations are further described below in Examples XIVthrough XVII, the overall structures of which are summaries in Tables 2and 3.

TABLE 2 Layer overview (thicknesses in nm) Example Example ExampleExample Layers XIV XV XVI XVII Barrier (on signal 4.00 4.00 4.00 4.00DBR side) QW 8.35 8.35 8.35 8.35 Barrier 83.00 83.00 83.00 97.30 QW 8.358.35 8.35 8.35 Barrier 24.00 24.00 24.00 QW 8.35 8.35 8.35 Barrier 8.0040.35 8.00 8.00 QW 8.35 8.35 8.35 8.35 Barrier 24.00 24.00 82.85 68.55QW 8.35 8.35 Barrier 50.50 50.50 QW 8.35 8.35 8.35 8.35 Barrier 24.0024.00 24.00 24.00 QW 8.35 8.35 8.35 8.35 Barrier 8.00 8.00 8.00 8.00 QW8.35 8.35 8.35 8.35 Barrier 24.00 24.00 24.00 24.00 QW 8.35 8.35 8.358.35 Barrier (on the air 25.10 25.10 25.10 25.10 side) Total length=349.75 349.75 349.75 349.75

TABLE 3 Barrier Layer thickness(es) and Other Geometry in units of a QWthickness Example Example Example Example Layers XIV XV XVI XVII Barrier(on signal 0.48 0.48 0.48 0.48 DBR side) QW 1.00 1.00 1.00 1.00 Barrier9.94 9.94 9.94 11.65 QW 1.00 1.00 1.00 1.00 Barrier 2.87 2.87 2.87 QW1.00 1.00 1.00 Barrier 0.96 4.83 0.96 0.96 QW 1.00 1.00 1.00 1.00Barrier 2.87 2.87 9.92 8.21 QW 1.00 1.00 Barrier 6.05 6.05 QW 1.00 1.001.00 1.00 Barrier 2.87 2.87 2.87 2.87 QW 1.00 1.00 1.00 1.00 Barrier0.96 0.96 0.96 0.96 QW 1.00 1.00 1.00 1.00 Barrier 2.87 2.87 2.87 2.87QW 1.00 1.00 1.00 1.00 Barrier (on the air 3.01 3.01 3.01 3.01 side)Total length= 41.89 41.89 41.89 41.89

Example XIV

In this MQW structure 5800, referred to as “1+3×121” or “1-121-121-121”and schematically shown in FIG. 58, the two-MQW-unit gain structure ofFIG. 54 (with each of the MQWs containing non-equidistantly-spaced 4individual QWs) was expanded with a third equivalently-configured MQWunit. As a result, the structure 5800 includes three identical, equal toone another MQW units 5810A, 5810B, 5810C (each positioned around acorresponding antinode of the standing electrical field formed duringthe operation of the VECSEL employing the structure 5800, and eachhaving the non-equidistantly-grown QWs A, B, C, and D formed asdiscussed in reference to FIG. 54) and a an additional stand-alone,single, “gain-boosting” QW E at the side of the signal DBR. A shape(with a FWHM width of 61.6 fs) and phase of the corresponding pulse,calculated to be generated during the operation of the VECSEL structureis illustrated in FIG. 59. This implementation (and otherimplementations structurally similar to this one) provide an answer tosimultaneous reduction of growth-related dislocations and increase ofgain available to the carriers.

Example XV

Notably, non-equidistantly-spaced-QW MQW units of the invention do nothave to have symmetric structure or be structured identically to avoidthe formation of dislocations causing loss of efficiency of lasing ofVECSEL structured employing such MQW units. FIGS. 60 and 61 illustrate,respectively, the gain portion of the VECSEL structure and thecalculated mode-locked pulse parameters (with a FWHM of 55.1 fs) of anembodiment the symmetry of which is “broken” as compared to that of theembodiment of a MQW unit of the embodiment 5400. Here, the gainstructure 6000 includes a MQW unit 6010 (configured in a fashionequivalent to that of the MQW unit 5810A, for example), and a MQW unit6020 having only three non-equidistantly disposed QWs A, C, and D(separated by barriers with unequal thicknesses d₄ and d₃). Thisimplementation, containing the stand-alone QW E (and otherimplementations structurally similar to this one) provide an answer tosimultaneous reduction of growth-related dislocations and increase ofgain available to the carriers.

Example XVI

In this example, in comparison with the example of FIG. 54, while firstMQW unit 6210 of the two MQWs of FIG. 62 is configured identically tothe MQWs 6010 and 5410B (with individual QWs A, B, C, and D that arenon-equidistantly-spaced as discussed above), the second MQW 6220includes only the individual QWs A, B, and C separated by barriers withunequal thicknesses of d, and dz. The corresponding pulse parameters areshown in FIG. 63. This implementation (and other implementationsstructurally similar to this one) provide an answer to simultaneousreduction of growth-related dislocations and increase of gain availableto the carriers.

Example XVII

Provides yet another related illustration to the structure-variationalstability of the proposed non-equidistantly-spaced-QW solution to theproblem of growth-cause dislocations of the VECSEL structure of theinvention. Here, while the gain structure 6400 of FIG. 64 is shown tocontain MQW units 6210 and 6420 (where the MQW 6420 is structurallyidentical to the MQW unit 6220), the MQW 6420 as a whole is configuredto be separated from the MQW 6210 by a barrier with a thickness Δ2 thatis different from and smaller than a thickness Δ1 of the barrierseparating the corresponding MQW units in the structure 6200.Specifically, the MQW unit 6420 as a whole is disposed such that, inoperation, its center of gravity is closer to the corresponding antinode6430A of the electrical field distribution 6430 in comparison to that ofthe MQW unit 6220 with respect to the antinode 6230A of the electricalfield distribution 6230 of FIG. 62. While such disposition leads to evenmore asymmetry of the overall gain structure, the resulting mode-lockedregime of operation of the corresponding VECSEL was calculated to remaina ‘ultra-short pulse” operation with the FWHM of a pulse to be 55.1 fs(see FIG. 65).

Despite multiple variations introduced both in the spatial symmetry andQW-content of at least one of the MQW units of the gain structure of theinvention, each of the structures 5200, 5400, 5800, 6000, 6200, and 6400(of FIGS. 52, 54, 58, 60, 62, and 64, respectively) proved to produce amode-locked ultra-short pulse operation with a pulse width or durationthat is barely changed from case to case. This is the evidence that theproposed “non-equidistant-QW” solution to the practical, empiricallyobserved problem of the growth dislocations limiting the lasingoperation of the VECSELs, is stable, operationally robust, andrepeatable. It is readily appreciated by a skilled artisan that as faras design is concerned, when a certain individual QW is “removed” from agiven MQW unit the total gain is somewhat reduced, so to compensate forthis the number of carriers in the remaining QWs has to be adjustedaccordingly in order to ensure that the gain from the structure isapproximately the same in all cases.

It should be understood that neither the scope of the invention nor theefficiency of the solution to the problem of dislocations stated aboveare affected by a particular distribution of the individualnon-equidistantly spaced QWs in a given MQW unit and/or by the sequencein which different MQW units (whether having the same of differentindividual QW content) are formed along the axis of the gains structure.For example, and in reference to FIG. 60 and embodiment 6000, theprinciple of operation and the scope of the invention is not affected ifthe locations of MQWs 6010 and 6020 are interchanged. Neither is thescope of the invention changed if the QW-content of any of the MQW units6010 and 6020 changed (for example, if the MQW unit 6010 is configuredto have five or more individual non-equidistantly-spaced QWs instead offour as in the example of FIG. 60, or if, for instance, the MQW unit6020 is modified to include QWs A, B, and D instead of its currentcontent of QWs A, C, and D). To provide another non-limitingillustration, and now in reference to FIG. 58, the scope of theinvention does not change if the number of the MQW units (eachcontaining at least three non-equidistantly-spaced from one anotherindividual QWs) is increased above three (as currently shown in FIG. 58)and/or any of such MQW units is modified to have its own, unique,not-repeated in another MQW unit content of non-equidistantly spacedQWs. For example, the embodiment 5800 can be modified to have 4 MQWunits 5810A, 5810B, 5810C and 5810D (not shown), while the MQW unit5810A includes the QWs A, B, C, and D as currently shown, the MQW unit5810B includes QWs A, B, and C, the MQW unit 5810C includes QWs B, C,and D, while the MQW unit 5810D includes 9 (nine)non-equidistantly-space QWs. The same general consideration applies tothe embodiments such as that of FIG. 52, which are devoid of thestand-alone QW (such as the QW E of FIGS. 58, 60) located in proximityto the signal DBR reflector.

It is appreciated, therefore, that specific implementations of the gainstructure—the ones that include a MQW configured according to an idea ofthe invention with respect to the immediately-neighboring nodes of thestanding wave of the electrical field (present in the laser cavityduring its operation) and containing at least three constituent QWs(which may be non-equidistantly spaced)—are characterized by at leasttwo (in the case of three QWs in the MQW unit) or more (in the case theMQW unit includes more than three QWs) barrier layers and at least twoor more of corresponding ratios ofbarrier-thickness-to-constituent-QW-thickness. A first barrier thicknessis different from the second barrier thickness when the constituent QWsare spaced substantially non-equidistantly. Generally, the ratio of athickness of the first barrier layer of the MQW unit to that of thesecond barrier layer of the MQW unit falls within a range from about0.01 to about 1; or within a range from about 0.1 to about 1 in aspecific implementation, or within a range from about 0.5 to about 1 inanother specific implementation. Alternatively or in addition, a firstratio of a barrier-thickness-to-constituent-QW-thickness may bedifferent from a second ratio of abarrier-thickness-to-constituent-QW-thickness when the constituent QWsare spaced substantially non-equidistantly. The difference between thesetwo ratios is generally between about 0.01 and 1 of the first of suchratios, or between 0.1 and 1 of the first of such ratios in a specificcase, or between 0.5 and 1 of the first such ratios in a relatedspecific case.

In case of any implementation, and in addition to the strain management,and according to the idea of the invention, the new VECSEL chip designsmay contain a series of passive layers in the region between the gainmedium and the external interface with air. FIGS. 66, 67 illustrate the“1-121-121” active gain element 5400 of FIG. 54 (which includes again-booster QW 6610 next to the node “ND” of the electric field 6710 inthe vicinity of the signal DBR 6630 combined with the two MQW units)embedded between a signal DBR 6630 on the left of FIGS. 66, 67 and aseries of semiconductor layers 6640 on the right with an added layer6644 of SiO₂; the latter constitute an anti-reflection (AR) coating. Thedistributed Bragg reflector 6630 is a DBR structure for operation at asignal wavelength, and only a few layers of it are shown in FIG. 66.Indicated in FIG. 66 are also typical layer thicknesses for a laserstructure designed to emit at a central wavelength of 980 nm. Typicallythe DBR 6630, needed to reflect light at such a central wavelength andsupport reflection of a broad band of nearby wavelengths sufficient tosupport a very short pulse, will include about 25 AlGaAs/AlAs repeats.Furthermore, an additional, pump DBR structure (not shown in FIG. 66)judiciously configured to back-reflect the external pump light(typically at a wavelength around 800 nm) can be added to the back ofthe signal DBR 6630 to contain about the same (or slightly smaller)number of alternating layers. Typical but non-limiting layer thicknessesare shown to be about 83 nm for Al layer and about 71 nm for AlGaAslayer.

Another related option for the design of an AR-coating for theembodiment of the invention is a multi-layer dielectric coatingoptimized to reduce the group delay dispersion (GDD) of the overalllaser structure. FIG. 67, for example, shows one implementation 6744 ofa sSi₃N₄/SiO₂ dielectric coating replacement for the AR coating 6644) ofFIG. 66, designed for a central wavelength of operation of 980 nm. Here,the InGaP cap semiconductor layer 6740 that terminates the semiconductorportion 5400 of the gain structure.

As has been already alluded to above, the SESAM can be implemented inaddition to the cap and AR-coatings, in the overall laser structurecontaining the intentionally-non-equidistantly-spaced-QW MQWs of theinvention, to minimize the absolute value and to flatten the wavelengthdependence of the GDD characterizing the VECSEL/MQW cavity. In oneembodiment, a SESAM design 6800 requires a single semiconductor quantumwell 6810 grown on a spacer layer 6820 and an appropriate reflector 6830(such as a DBR), as shown in a specific and non-limiting example ofFIGS. 68A, 80B.

As shown, the SESAM 6800 abuts a top Si₃N₄ AR-coating 6820. The firstlayer 6840 of the semiconductor structure (adjacent to the single QW6810) may be about 2 nm to 7 nm thick to allow for fast carrierrecombination, which is necessary to generate short pulses. The singleQW 6810 will typically have a design to that of a QW in the active gainportion of the structure (that is, a QW in a MQW unit located to theleft of the SESAM as viewed in FIGS. 68A, 68B) but, in comparison, withthe central absorption wavelength tuned to a shorter wavelength (with atypical detuning value of several nm, for example up to 1 to 5 nm; or ina related example up to 10 nm).

The proposed herein GDD-targeted optimization of passive elements of theoverall structure to match active gain element and nonlinear SESAM GDDand structured configured as a result of such process have not beendiscussed in related art up to-date, to the best knowledge of theinventors. Convergence to a final full cavity design that produces theshortest time-bandwidth limited mode-locked pulse requires that allfully optimized cavity components (active and passive) including gain,absorption and GDD, should be part of the full microscopic simulation ofthe device, some additional details of which can be found in referred toI. Kilen, J. Hader, J. V Moloney, and S. W. Koch, UltrafastNonequilibrium Carrier Dynamics in Semiconductor Laser Mode-Locking,Optica (2014), incorporated herein in by reference in its entirety.

Illustrations presented in FIGS. 69, 70, 71, 72, 73, 74, and 75 expandon the implementation of the idea of a gain-boosting QW addition to theMQW-based gain structure of the invention (whether the constituent QWsin the MQW-based structure are spaced equidistantly, within a given MQW,or non-equidistantly). Here, the comparison is made among different gaincurves calculated, for the operating wavelength of 1030 nm, with thecurve 6920 of FIG. 69, calculated for the RPG-based gain region 7110 ofFIG. 71 (in which the RPG structure 7110 is surrounded by a chosensignal DBR reflector indicated at the left of the FIG. 69, and thecombination of chosen cap, AR, and SESAM on the right of the FIG. 69; byanalogy with that of FIG. 1).

Curve 6920 represents the gain of the MQW structure 7220 of FIG. 72,which contains 3 MQW units (each designed to be located between theimmediately-neighboring nodes of the electrical field, in operation ofthe corresponding VECSEL, and each containing four equidistantly spacedconstituent QWs). Curve 6930 corresponds to the gain curve of the MQWstructure 7330 of FIG. 73, which contains 3 MQW units of FIG. 72 and anadditional, stand-alone QW “Q” in the vicinity of the antinode of thestanding electrical field). It can be easily verified, from thecomparison of the curves 6910, 6920, 6930 of FIG. 69, that the additionof the “gain-boosting” QW “Q” leads to increase of the gain to offsetother competing losses such as output coupler (outcoupler) losses andSESAM saturable losses within the overall laser cavity.

Curve 7020 represents the gain of the MQW structure 7420 of FIG. 74,which contains 3 MQW units (each designed to be located between theimmediately-neighboring nodes of the standing electrical field, inoperation of the corresponding VECSEL, and each containing fournon-equidistantly spaced constituent QWs). Curve 7030 represents thegain of the MQW structure 7530 of FIG. 75, which is structured byanalogy with that of FIG. 58 and which contains 3 MQW units of thestructure of FIG. 74 complemented with a stand-alone near the signal DBRreflector “gain-boosting” QW, labelled as “R”. It can be easilyverified, from the comparison of the curves 6910, 7020, 7030 of FIG. 70,that the addition of the “gain-boosting” QW “R” leads to increase of thegain to offset other competing losses such as outcoupler losses andSESAM saturable losses within the overall laser cavity.

Structural and material details pertaining to the gains regionscorresponding to 7110, 7220, 7330, 7420, and 7530 are summarized inTable 4.

The layer designs were as follows: 0. Phase: GOLD 100 nm, 65 nmInGaP; 1. Signal DBR (12 repeats of): 76 nm AlGaAs and 88 nm AlAs; 2.Chosen GAIN STRUCTURE; 3. AR coating: 162 nm InGaP, 182 nm Si3N4 and 248nm SiO2.

Notably, for the calculation the carrier densities for the “equidistantQW” structures 7220 and 7330 are slightly higher than those for thenon-equidistant counterparts 7420 and 7530:

QW density: In units [10¹⁶ m⁻²]: 2.24 (for RPG 6910); 2.83 (for 7220 and7330); and 2.75 (for 7420 and 7530). This was done to reflect thepractical situation and to be able to compare the two structuresrelative to the gain provided by the RPG12 structure 6910.

TABLE 4 GAIN STRUCTURES (Width of layers in nanometers) RPG12 MQW 3x4MQW 1 + 3X4 MQW 3x121 MQW 1 + 3x121 GaAsP 4.08 4.08 QW (Booster) 8.358.35 GaAsP 137.91 96.49 83.91 96.63 83.91 QW 8.35 8.35 8.35 8.35 8.35GaAsP 140.24 18.96 18.96 24.31 24.31 QW 8.35 8.35 8.35 8.35 8.35 GaAsP140.22 18.86 18.86 8.16 8.16 QW 8.35 8.35 8.35 8.35 8.35 GaAsP 140.2218.96 18.96 24.31 24.31 QW 8.35 8.35 8.35 8.35 8.35 GaAsP 140.22 57.8257.84 57.84 57.84 QW 8.35 8.35 8.35 8.35 8.35 GaAsP 140.22 18.96 18.9624.31 24.31 QW 8.35 8.35 8.35 8.35 8.35 GaAsP 140.22 18.86 18.86 8.168.16 QW 8.35 8.35 8.35 8.35 8.35 GaAsP 140.22 18.96 18.96 24.31 24.31 QW8.35 8.35 8.35 8.35 8.35 GaAsP 140.22 57.92 57.89 57.89 57.89 QW 8.358.35 8.35 8.35 8.35 GaAsP 140.22 18.96 18.96 24.31 24.31 QW 8.35 8.358.35 8.35 8.35 GaAsP 140.22 18.86 18.86 8.16 8.16 QW 8.35 8.35 8.35 8.358.35 GaAsP 140.22 18.96 18.96 24.31 24.31 QW 8.35 8.35 8.35 8.35 8.35GaAsP 71.76 40.95 41.11 40.81 41.11

Robust Lasing Operation

Notably, a stunningly advantageous feature of the cumulative MQWarchitecture of the present invention is the remarkable robustness ofthe non-equilibrium pulsed laser system (that utilizes an embodiment ofthe cumulative MQW structure) to changes in the SESAM absorption andoutcoupler losses. In fact, it has been discovered that these changesmay be varied in magnitude while the overall system retains the sameeffective available gain bandwidth without materially changing theoutput pulse characteristics. This observation confirms the result thatthe mode-locking once established continues primarily from efficientlyextracting all or most available carriers.

FIG. 35 shows a linear gain (line 35.1), SESAM absorption (line 35.2)and net linear gain spectra (line 35.3) for the situation where thecarrier density is reduced from 5×10¹⁶ m⁻² to 4.5×10¹⁶ m⁻². FIG. 36shows a linear gain (line 36.1), SESAM absorption (line 36.2) and netlinear gain spectra (line 36.3) for the situation where the outcouplingloss is increased from 2% to 2.8%, comparable with FIG. 28.

In FIGS. 27-30, which leads to a 23.8 fs pulse waveform, a relativelylarge SESAM absorption is employed as was in the other examples. The netlinear gain bandwidth in FIG. 28 is 157 meV. The SESAM absorption inFIG. 35 is now reduced and carrier density adjusted in the MQW to4.5×10¹⁶ m⁻² so as to maintain approximately the same net linear gainbandwidth of 157 meV as in FIG. 28. The outcoupling loss is adjustedfrom 2% to 2.8% and similarly the inversion adjusted in the MQW toretain the same 157 meV linear net gain bandwidth in FIG. 36.

FIG. 37 shows a spectrum of the final mode-locked pulse corresponding toFIG. 35. FIG. 38 shows a spectrum of the final mode-locked pulsecorresponding to FIG. 36. In both FIG. 37 and FIG. 38, the shaded areain both pulses is the net linear gain bandwidth.

FIGS. 37 and 38 show the mode-locked pulse spectra for both casesdepicted in FIGS. 35 and 36. The shapes are again strongly distorted dueto the strong amplification in the structure but they again both mimicthe full linear gain bandwidth rather than the net linear gainbandwidth.

FIG. 39 shows a mode-locked pulse of duration 27 fs corresponding toFIGS. 35 and 37. FIG. 40 shows a mode-locked pulse of duration 28.1 fscorresponding to FIGS. 36 and 38. Some of the spectral distortionspresent in FIGS. 37 and 38 are due to the residual satellites appearingon the trailing edge of each pulse in FIGS. 39 and 40. These can besuppressed significantly by replacing the dispersive single layercoating employed in simulations here by multi-layer AR-coatings thatfurther flatten the dispersion. Some of the spectral distortion is dueto the fact that the MQW arrangement is not optimized to effectivelyremove the entire carrier inversion and some unused carriers can causethe appearance of such satellite sub-pulses.

The results in FIGS. 35-40 show that changing the SESAM absorption oroutcoupling loss does not fundamentally change the outcome of the pulsemode-locking. This is not surprising, as the final nonequilibrium andnonlinear dynamical system is dominated by the almost entirely evacuatedcarrier subsystems. Additionally MQW pulse energies and repetition ratescan be scaled up by extending the cavity length from the very short 3.2cm cavity used here to longer or even shorter cavities. See for examplereference to such scaling of the MIXSEL structure by Mario Mangold,Christian A. Zaugg, Sandro M. Link, Matthias Golling, Bauke W. Tilma,and Ursula Keller, Pulse repetition rate scaling from 5 to 100 GHz, Opt.Exp., 22, 6099 (2014) with a high-power semiconductor disk laser, Opt.Exp., 22, 6099 (2014), incorporated herein by reference in its entirety.

It is appreciated, therefore, that an implementation of the presentinvention results in a method for generating light pulses in asurface-emitting semiconductor laser system configured to operate in amode-locked regime. Such method includes pumping a semiconductor gainmedium (of a semiconductor laser chip disposed within an opticalresonator of said laser system) with an output from a pump source tocreate excited carriers within a bandwidth of a full gain spectrum ofsaid semiconductor medium (where said full gain spectrum has a bandwidthcontaining a first wavelength). The method further includes forming astanding wave within the laser chip at a frequency of the firstwavelength. The standing wave defines first and second immediatelyneighboring nodes located along the optical axis within the gain medium.Additionally, the method includes multiply transmitting light, formedwithin an optical resonator, through a first MQW unit in the gainmedium, while such first MQW unit includes at least three first QWsseparated from one another by a sub-wavelength distance, all of suchthree or more first QWs are disposed between the first and second nodesof the standing wave. A method may further include steps of traversingsuch light through a mode-locking element of the laser system to achievelight-pulses the duration of each of which does not exceed 100 fs; andoutcoupling a train of light-pulses through a reflector of the opticalresonator. The optical resonator of the present laser system may containa reflector defined by a distributed Bragg reflecting structure in asemiconductor chip and a simple reflector (which term is defined torefer to a dielectric thin-film-stack mirror or metallic mirror such asa first-surface mirror). Optionally, the method also contains a step ofmultiply transmitting light through a second MQW unit in the gainmedium, such second MQW unit containing at least one second QW, andwhere the second MQW unit is separated from the first MQW unit by atleast one node of the standing wave. Furthermore, the method may includea process of extracting excited-state carriers at frequencies thataggregately define a majority of a bandwidth of a full gain curve of thegain medium.

Embodiments of a Pumping System

Many different pumping schemes can be used to realize the resultsdiscussed herein related to the MQW laser architecture. Semiconductordisk lasers can be pumped in a variety of ways. A typical opticalpumping scheme for mode-locking is shown in FIG. 41 where a fibercoupled fiber bar or, alternatively, a single mode lower power pump beamis imaged onto the surface of the semiconductor chip. In this example, aconventional semiconductor disk laser (VECSEL RPG structure) ismode-locked using a commercial semiconductor saturable absorber mirror(SESAM). The same set-up can be used with the present inventive MQWlaser.

FIG. 41 shows a schematic layout of a typical external optically-pumpedV-cavity for generating mode-locked pulse trains.

FIG. 42 shows an autocorrelation measurement of the sub-picosecondmode-locked high average power pulse.

FIG. 43 shows an exemplary QW energy level diagram of optical pumping ofa barrier region having a large quantum defect ΔE=(ℏω_(p)−ℏω). FIG. 44shows an exemplary QW energy level diagram of optical pumping the upperstate in the quantum well having a much smaller quantum defectΔE=(ℏω−ℏω).

FIG. 41 shows a V-cavity optical pumping geometry which is just one ofmany possible pumping geometries. One of ordinary skill in the art willrecognize that other pumping geometries can be employed, including:linear cavity, z-cavity, etc. FIG. 42 shows an experimentally measuredcorrelation trace of a mode-locked pulse generated from the V-cavitygeometry shown in FIG. 41 and taken from reference M. Scheller, T.-L.Wang, B. Kunert, W. Stolz, S. W. Koch, and J. V. Moloney, “Passivelymode-locked VECSEL emitting 682 fs pulses with 5.1 W of average outputpower,” Electronics Letters, 48, 588-589 (2012) incorporated herein inby reference in its entirety.

The optical pump can by at a wavelength that either pump the barriers orpump QWs directly. In the typical barrier-pumped RPG structure,approximately 80% of the incident pump power is absorbed in a singlepass through the chip. In-well pumping leads to much smaller absorptionper pass through the structure but also generates much less waste heatdue to the smaller quantum defect. Typically QW pumping of an RPGrequires multiple passes (at least 2) through the structure. FIGS. 43and 44 show contrasting pump wavelengths for two optical pumpingscenarios. An in-well pumping scheme has been employed by Wei Zhang,Thorsten Ackemann, Stephen McGinily, Marc Schmid, Erling Riis, andAllister I. Ferguson (see “Operation of an optical in-well-pumpedvertical-external-cavity surface-emitting laser, Appl. Opt., 45, 7729,2006) to generate near-IR wavelength of 855 nm using a GaAs basedmaterial system and incorporated herein by reference in its entirety. Asimilar in-well and barrier pumping scheme has been employed by J.Wagner, N. Schulz, M. Rattunde, C. Ritzenthaler, C. Manz, C. Wild, andK. Kohler, Barrier-and in-well pumped GaSb-based 2.3 μm VECSELs, phys.stat. sol. (c) 4, 1597-1600 (2007) to generate mid-IR wavelength of 2.3μm using a GaSb-based material system and incorporated herein byreference in its entirety.

A related pumping scheme can be configured with the use of an externalpulsed laser source to synchronously pump the embodiment of thecumulative MQW structure. Such an external pumping scheme has beenemployed by Wei Zhang, Thorsten Ackemann, Marc Schmid, Nigel Langford,Allister I. Ferguson, Femtosecond synchronously mode-lockedvertical-external cavity surface-emitting laser, Opt. Exp., 14, 1810(2006), incorporated herein by reference in its entirety, where acomplex multiple pass cavity arrangement.

The reader is referred to a comprehensive review of possible pumpschemes (barrier, in-well and electrical), cavity geometries andreported results with comprehensive referencing is provided inSemiconductor Disk Lasers: Physics and Technology (Oleg G. Okhotnikov,Editor; 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim; ISBN:978-3-527-40933-4), which is incorporated herein by reference in itsentirety.

Because MQWs are significantly thinner than the usual RPG, MQWsconsequently can operate when even less pump power is absorbed in asingle pass (for example the above 8 QW MQW would absorb between 15-20%of the pump in a single pass even when barrier pumped). Well pumpingcould lead to comparably smaller absorption. In the barrier pumped case,it would be possible to grow an extra DBR at the back of the signal DBRto reflect the pump light for a 2-pass configuration. With in-wellpumping, the DBR stopband for the signal could be arranged to alsoreflect the shorter wavelength pump light. An even better solution wouldbe to have a gold (Au) or other high reflection metallization layerdeposited at the back end of the signal DBR. A thin few nm thick layerwould act as an efficient reflector for both a barrier or QW pump.

A possible multi-pass pump geometry that is commonly used in opticallypumped thin disk lasers could be set up to efficiently barrier- orwell-pump the semiconductor MQW chip. FIG. 45 depicts a possiblemulti-pass geometry where a parabolic mirror and multiple prisms act tosplit the incoming pump beam into multiple pump beams simultaneouslyimpinging on the laser chip. The thin disk crystal would be replaced bythe novel MQW semiconductor disk chip. As shown in FIG. 46, the latterwould be bonded to a CVD diamond heat spreader and water-cooled copperheat sink, employing a standard bonding technique. This is one of manypossible realizations for multiple pass pump geometries.

The ultimate compact pumping geometry involves an electrically pumpedMQW chip. This offers the most compact pumping arrangement and would bewell suited to the thin semiconductor MQW chip. The electrical pumpingsetup depicted in FIG. 47 will involve added complications such as extraJoule heating, losses due to DBR p- and n-doping and an additional uppern-doped DBR. The structure depicted in this figure is just one possiblerealization of an electrically pumped configuration. In thisrealization, the bottom DBR is p-doped and a top short DBR is n-doped.Additionally, there needs to be a current spreading layer from the topcontact that facilitates a relatively uniform current flow in the centerof the chip. Details of a possible implementation of such anelectrically pumped VECSEL are given by Y. Barbarian, M. Hoffmann, W. P.Pallmann, I. Dahhan, P. Kreuter, M. Miller, J. Baier, H. Moench, M.Golling, T. Sudmeyer, B. Witzigmann, and U. Keller, Electrically PumpedVertical External Cavity Surface Emitting Lasers Suitable for PassiveModelocking, IEEE J. Sel. Top. In Quant. Electron., 17, 1779 (2011),incorporated herein by reference in its entirety.

The high repetition rates achievable with semiconductor sources willmake the MQW structures particularly useful for LIDAR, optical arbitrarywave-form generation, advanced ultra-high bandwidth communicationsystems, semiconductor inspection and coherent detection applications.Additionally such a source could be used in medical and biologicalapplications with one example being OCT (Optical Coherence Tomography)and another multiphoton microscopy (bio-imaging) for new “red” classesof dyes/markers. For a comprehensive review of potential applications inmedicine and biology see the text Ultrashort Pulses in Biology andMedicine, Editors: Markus Braun, Peter Gilch and Wolfgang Zinth, ISBN-13978-3-540-73565-6 (Springer Berlin Heidelberg New York), incorporatedherein by reference in its entirety, where applications are specific tothe current generation of solid state lasers. Mode-locked laser based onthe proposed MQW structure can replicate these systems at theiroperating wavelengths in a possibly more compact geometry and extendinto application areas needing currently inaccessible wavelengthsources.

VECSEL sources in particular have been shown to exhibit very goodquantum-limited noise performance, especially compared to doped fiberlaser counter-parts. Such low noise performance in a compact mode-lockedsource could prove to be the ideal frequency comb source. Applicationsinclude improved and field-usable clocks and ultra-low noise microwavegeneration for improved timing and synchronization in communication,navigation, and guidance systems.

It is appreciated, therefore, that implementations of the inventionprovide a specifically-designed surface-emitting semiconductor lasersystem, which includes a semiconductor laser chip disposed in aresonator cavity and comprising a semiconductor gain medium and a mirrorattached to the semiconductor gain medium. An active part of thesemiconductor laser chip has an optical path length along an opticalaxis which corresponds to multiple wavelengths of light in thesemiconductor medium and is configured to produce, when pumped by anappropriate source, a standing wave at a wavelength λ corresponding to afrequency from the gain spectrum of the gain medium.

The semiconductor gain medium includes a first plurality of quantumwells that are stacked on each other along the optical axis withintermediate spacings of the order of the thickness of the quantum wellsto form a multiple quantum well gain element that, in a specific case,spans the majority of a distance representing a half-cycle of thestanding wave. The gain medium can be configured such as to include suchmultiple-quantum-well gain element is repeated multiple times. Thesemiconductor laser chip optionally has an anti-reflection coating tosuppress spurious reflections. The plurality of quantum wells can span aplurality of half-cycles of the standing wave formed within the cavity.The sequence of QWs forming one base MQW unit of the MQW structure ofthe invention can include any specific number of QWs, starting from atleast 3 QWs to 10 QWs. Specific examples of numbers of QWs forming oneMQW unit include 3, 4, 5, 6, 7, 8, 9, and 10 QWs. The cumulative MQWstructure of an embodiment of the invention may include an integernumber of the MQW units (specific examples include 1, 2, 3 4 and 5 MQWunits) such that the plurality of quantum wells in the overall,cumulative MQW structure contains any specific number of QWs between 3QWs and 60 quantum wells.

The gain medium is configured such as to substantially completelybleaches out the inversion generated in the gain medium by the pumpsource. A spacing between immediately adjacent quantum wells in thecumulative MQW structure of the invention is in the range from about0.01 to about 0.15 times the wavelength λ. It is noted that, generally,not all spacings between the QWs in a MQW structure of the inventionhave to be equal. A sub-wavelength spacing between adjacent quantumwells can be sufficiently large to provide sufficiently strong quantumconfinement of the carriers to the individual quantum wells, thusconstituting a multiple quantum-well structure with each structurehaving quantized states existing within the individual quantum wells andspatially confined by the energy barrier provided by the separationlayers. By “sufficiently large,” the separation layers between the QWshave thicknesses on the order of 1 to 100 nm, or 5-12 nm, or 1-5 nmdepending on the insulating characteristics of the separation layerbetween the quantum wells. Alternatively or in addition at least onsub-wavelength spacing between adjacent quantum wells of a plurality ofquantum wells can be less than a thickness of the individual quantumwells such that some or all of the carrier wavefunctions are delocalizedover more than one quantum well thus constituting a superlatticestructure.

Alternatively, a sub-wavelength spacing between adjacent quantum wellsof the plurality of quantum wells is chosen in the range between 0.01and 0.25 times λ/n, where n is an average refractive index of thesemiconductor gain medium; in a related embodiment—in the range 0.01 and0.35 times λ/n.

Optionally, in one implementation, the surface emitting semiconductorlaser system includes a pump source configured to pump energy into thesemiconductor gain medium to produce excited-state electrons in thequantum wells, and a mode-locking element included in the resonatorcavity to mode-lock the resonator cavity and to extract lightamplification in the form of ultrashort pulses, and an output couplerthrough which such ultrashort light pulses are transmitted outside thecavity. The mode-locking element can include at least one of asemiconductor saturable absorber mirror element, a self-phase modulationKerr lens element, and an active modulation element.

The semiconductor gain medium can include a base material that is acompound semiconductor that includes a combination of elements from thegroups III and V or the groups II and VI of the periodic table. Thesemiconductor gain medium can include a second plurality of quantumwells positioned relative to adjacent quantum wells thereof at a secondsub-wavelength spacing of the center wavelength λ.

The first plurality of quantum wells can be disposed such that, withrespect to a center of the half-cycle of the standing wave formed duringthe lasing operation along the optical axis, a group of such QWs islocated asymmetrically (in other words, closer to one of the nodescorresponding to this half-cycle than to another nodes corresponding tothis half-cycle).

Alternatively or in addition, there can be included a second pluralityof quantum wells such that the first plurality of quantum wells aredisposed within one half of a wavelength cycle of the wavelength λ, andthe second plurality of quantum wells are disposed within the other halfof the wavelength cycle of the wavelength λ. In this configuration, thesecond plurality of quantum wells can be offset, along the optical axis,from the antinode of the standing wave by a pre-defined distance.

The optical resonator of the laser system can be an extended resonatorwith a gap between the semiconductor laser chip and the output coupler.The gap can be filled with gas (such as air for example, or nitrogen) orliquid (such as a cooling liquid or an index-matching liquid).

In a different aspect of the invention, there is provided a resonatorstructure for generation of stimulated emission. The resonator structureincludes a semiconductor gain medium having a plurality of quantumwells. The plurality of quantum wells can include one or more onequantum wells disposed offset a substantial distance from an anti-nodeof the resonant cavity. A sub-wavelength spacing between adjacentquantum wells of the plurality of quantum wells is in the range 0.01 and0.15 times the center frequency wavelength λ/n, where n is an averagerefractive index of the semiconductor gain medium.

There is additionally provided a method for generation of stimulatedemission from the lasers and resonant structures noted above. The methodincludes pumping the semiconductor gain medium structured according toan embodiment of the invention to form excited state electrons in thegain medium. The method further includes extracting carriers from theexcited states in the gain medium. In the method, the step ofamplification of light can include gainful utilization of the majorityof the inversion. In particular, amplification of light can beconfigured to extract between 1% to 5% of the inversion; preferably 1%to 65% of the inversion; more preferably 1% to 75% of the inversion;even more preferably 1% to 85% of the inversion from the gain medium;and even more preferably between 1% and 95% of the inversion, with anyspecifically defined intermediate ranges.

As present research indicates, the commonly-used and relied upon linearnet gain consideration plays little, if any, role in the cumulative MQWstructure and, as shown below, super intense pulses defined by operationof an embodiment of the invention continue to mode-lock even when thereis a net and sizeable linear absorption in the system. In other words,the system exhibits a strong hysteresis. Mode-locking elements such assemiconductor saturable absorbers, Kerr lensing or other activemode-locking contraptions and/or effects play a peripheral role asself-starting elements in an embodiment of the invention, and as a meansof sustaining the circulating pulses.

The mode-locking behavior of a cumulative MQW structure of discussedembodiments is not sensitive to the specific nature of the saturableabsorber (e.g., a SESAM with a DBR replacing the simple output coupler,a graphene mirror (GSAM), a Kerr Lens mode-locking or even self-KerrLens mode-locking (KLM)); nor is it sensitive to a manner in which amode-locking element is utilized (reflection or transmission mode).Neither does the mode-locking operation of an embodiment depend on theoverall cavity length beyond that dictated by the physics ofsemiconductor mode-locking.

By leaving relatively few unsaturated carriers behind, the additionalbenefit of a very robust system that can be driven harder without thelikelihood of causing pulse breakup can be obtained—pulse breakuptypically arises because reservoirs of unused carriers amplifysub-pulses after the growing pulse bleaches out carriers around itscentral frequency. Conventional RPG mode-locked systems leave very largereservoirs of unsaturated carriers behind due to inefficient extractionof carriers in narrow spectral windows. These RPG systems are limited inhow short a pulse they can generate, and are restricted to low gainsituations well below any bleaching threshold—as mentioned above,bleaching at high pump levels tends to destabilize the single pulse andcause pulse breakup as discussed in I. Kilen, J. Hader, J. V Moloney,and S. W. Koch, Ultrafast Nonequilibrium Carrier Dynamics inSemiconductor Laser Mode-Locking, Optica (2014), incorporated herein inby reference in its entirety, and observed experimentally by S. Husainiand R. G Bedford, Graphene Saturable Absorber for High PowerSemiconductor Disk Laser Mode-Locking, Appl. Phys. Letts, 104, 161107(2014), incorporated herein by reference in its entirety.

The MQW structure can be used with any semiconductor quantum well(s)that exhibits gain (inversion) under external pumping and consequentlycovers a broad swath of wavelengths, extending from the ultravioletthrough to the far infra-red, as well as a wide range of possiblesemiconductor material systems. For example semiconductor disk lasers(also referred to as Vertical External Cavity Surface Emitting Lasers(VECSELs)) have been demonstrated at UV, visible, near-IR and far-IRwavelengths using GaN-based, GaAs-based, GaSb-based and even PbTe-basedmaterial systems. Moreover, the MQW structure applies to all possiblemethods of optimizing either barrier (Step Index (STIN), Graded Index(GRIN)), quantum well (QW) or electrical pumping, because the MQWstructure provides the special quantum well arrangement that maximizesextraction of most or almost all carriers during the pulse transitthrough the chip.

References throughout this specification to “one embodiment,” “anembodiment,” “a related embodiment,” or similar language mean that aparticular feature, structure, or characteristic described in connectionwith the referred to “embodiment” is included in at least one embodimentof the present invention. Thus, appearances of the phrases “in oneembodiment,” “in an embodiment,” and similar language throughout thisspecification may, but do not necessarily, all refer to the sameembodiment. It is to be understood that no portion of disclosure, takenon its own and in possible connection with a figure, is intended toprovide a complete description of all features of the invention. Withinthis specification, embodiments have been described in a way thatenables a clear and concise specification to bet written, but it isintended and will be appreciated that embodiments may be variouslycombined or separated without parting from the scope of the invention.In particular, it will be appreciated that all features described hereinat applicable to all aspects of the invention.

In addition, when the present disclosure describes features of theinvention with reference to corresponding drawings (in which likenumbers represent the same or similar elements, wherever possible), thedepicted structural elements are generally not to scale, and certaincomponents are enlarged relative to the other components for purposes ofemphasis and understanding. It is to be understood that no singledrawing is intended to support a complete description of all features ofthe invention. In other words, a given drawing is generally descriptiveof only some, and generally not all, features of the invention. A givendrawing and an associated portion of the disclosure containing adescription referencing such drawing do not, generally, contain allelements of a particular view or all features that can be presented isthis view, at least for purposes of simplifying the given drawing anddiscussion, and directing the discussion to particular elements that arefeatured in this drawing. A skilled artisan will recognize that theinvention may possibly be practiced without one or more of the specificfeatures, elements, components, structures, details, or characteristics,or with the use of other methods, components, materials, and so forth.Therefore, although a particular detail of an embodiment of theinvention may not be necessarily shown in each and every drawingdescribing such embodiment, the presence of this particular detail inthe drawing may be implied unless the context of the descriptionrequires otherwise. In other instances, well known structures, details,materials, or operations may be not shown in a given drawing ordescribed in detail to avoid obscuring aspects of an embodiment of theinvention that are being discussed. Furthermore, the described singlefeatures, structures, or characteristics of the invention may becombined in any suitable manner in one or more further embodiments.

The invention as recited in claims appended to this disclosure isintended to be assessed in light of the disclosure as a whole, includingfeatures disclosed in prior art to which reference is made.

For the purposes of this disclosure and the appended claims, the use ofthe terms “substantially”, “approximately”, “about” and similar terms inreference to a descriptor of a value, element, property orcharacteristic at hand is intended to emphasize that the value, element,property, or characteristic referred to, while not necessarily beingexactly as stated, would nevertheless be considered, for practicalpurposes, as stated by a person of skill in the art. These terms, asapplied to a specified characteristic or quality descriptor means“mostly”, “mainly”, “considerably”, “by and large”, “essentially”, “togreat or significant extent”, “largely but not necessarily wholly thesame” such as to reasonably denote language of approximation anddescribe the specified characteristic or descriptor so that its scopewould be understood by a person of ordinary skill in the art. In onespecific case, the terms “approximately”, “substantially”, and “about”,when used in reference to a numerical value, represent a range of plusor minus 20% with respect to the specified value, more preferably plusor minus 10%, even more preferably plus or minus 5%, most preferablyplus or minus 2% with respect to the specified value. As a non-limitingexample, two values being “substantially equal” to one another impliesthat the difference between the two values may be within the range of+/−20% of the value itself, preferably within the +/−10% range of thevalue itself, more preferably within the range of +/−5% of the valueitself, and even more preferably within the range of +/−2% or less ofthe value itself.

The use of these terms in describing a chosen characteristic or conceptneither implies nor provides any basis for indefiniteness and for addinga numerical limitation to the specified characteristic or descriptor. Asunderstood by a skilled artisan, the practical deviation of the exactvalue or characteristic of such value, element, or property from thatstated falls and may vary within a numerical range defined by anexperimental measurement error that is typical when using a measurementmethod accepted in the art for such purposes.

Other specific examples of the meaning of the terms “substantially”,“about”, and/or “approximately” as applied to different practicalsituations may have been provided elsewhere in this disclosure.

While certain implementations have been described, these implementationshave been presented by way of example only, and are not intended tolimit the teachings of this disclosure. Indeed, the novel methods,apparatuses and systems described herein may be embodied in a variety ofother forms; furthermore, various omissions, substitutions and changesin the form of the methods, apparatuses and systems described herein maybe made without departing from the spirit of this disclosure.

What is claimed is:
 1. A surface-emitting semiconductor laser systemconfigured to operate in a mode-locked regime, the laser systemcomprising: an optical resonator having an optical axis; a semiconductorlaser chip within the optical resonator, the semiconductor laser chipcontaining a semiconductor gain medium, wherein said semiconductor gainmedium is characterized by a gain spectrum, the gains spectrum having abandwidth that includes a first wavelength, wherein said semiconductorgain medium has a first multiple quantum well (MQW) unit, said first MQWunit defined by a sequence of at least three first quantum wells (QWs)that are spaced substantially non-equidistantly with respect to oneanother; and a pump source in operable communication with saidsemiconductor laser chip and configured to pump energy to thesemiconductor gain medium to produce excited-state carriers in the firstMQW unit, wherein said semiconductor laser system is configured to forma standing optical wave within said semiconductor laser chip at afrequency of the first wavelength, said standing optical wave havingfirst and second immediately neighboring modes located along the opticalaxis within the semiconductor gain medium, said first and second nodesformed on the opposite sides of said first MQW unit.
 2. A laser systemaccording to claim 1, wherein the first MQW unit is positionedasymmetrically between the first and second immediately neighboringnodes.
 3. A laser system according to claim 1, further comprising amode-lock element disposed in optical communication with the laser chipand configured to define mode-locked pulses of optical radiation insidesaid optical resonator when said energy is pumped to the laser chip. 4.A laser system according to claim 3, wherein the mode-lock elementcomprises at least one of a semiconductor saturable absorber mirrorelement, a self-phase modulation Kerr lens element, and an activemodulation element.
 5. A laser system according to claim 1, wherein saidlaser system is configured to define durations, of said mode-lockedpulses, each of which durations is shorter than one hundredfemtoseconds.
 6. A laser system according to claim 1, wherein twoneighboring QWs from said at least three first QWs are separated fromone another by a first confinement barrier material, the firstconfinement barrier material having a first thickness that is smallerthan a thickness of a QW from the first QWs to delocalize at least onecarrier wavefunction over more than one first QW.
 7. A laser systemaccording to claim 1, wherein an overall thickness of said first MQWunit, measured along the optical axis, is greater than a half of adistance between the first and second immediately neighboring nodes ofsaid standing optical wave.
 8. A laser system according to claim 1,wherein the semiconductor gain medium includes a base material that is acompound semiconductor comprising a combination of elements from (i)groups III and V of the periodic table, or (ii) groups II and VI of theperiodic table.
 9. A laser system according to claim 1, wherein the pumpsource is configured to electrically create electrons in a conductionband of the semiconductor gain medium.
 10. A laser system according toclaim 1, wherein the pump source includes a (p-and-n) dopedsemiconductor chip.
 11. A laser system according to claim 1, furthercomprising an optical system configured as at least one of a single-passoptical pumping system, a multi-pass Z-cavity optical pumping system, amulti-pass V-cavity optical pumping system, and a linear cavity opticalpumping system, said optical system positioned to define opticalcommunication between the semiconductor gain medium and the pump sourceto create electrons in a conduction band of the semiconductor gainmedium with radiation from the pump source.
 12. A laser system accordingto claim 1, wherein said standing optical wave has third and fourthnodes located along the optical axis within the gain medium, said thirdand fourth nodes being immediately neighboring to one another, whereinsaid gain medium includes a second MQW unit, said second MQW unitcontaining at least one second QW, said second MQW unit located betweenthe third and fourth nodes, and wherein the pump source is configured topump energy to the gain medium to produce excited carriers in all MQWunits present in the laser system.
 13. A laser system according to claim12, wherein said at least one second QW includes at least three secondQWs that are spaced substantially non-equidistantly with respect to oneanother.
 14. A laser system according to claim 12, wherein a reflectorof the optical resonator includes a distributed Bragg reflector (DBR)integrated with the gain medium, wherein said second and third nodes areimmediately neighboring to one another such that the first, second,third, and fourth nodes form a sequence of nodes in which the first nodeis the closest to the DBR; wherein the first MQW unit includes fourfirst QWs, the second MQW unit includes at least three second QWs; andfurther comprising a third MQW unit containing multiple third QWs, saidthird MQW unit located between the second and third nodes.
 15. A lasersystem according to claim 14, QWs of at least one of the second andthird MQW units are spaced substantially non-equidistantly with respectto one another.
 16. A laser system according to claim 1, wherein saidstanding optical wave has a third node located along the optical axiswithin the gain medium, said second and third nodes being immediatelyneighboring with respect to one another, and wherein said gain mediumincludes a second MQW unit, said second MQW unit containing a sequenceof at least three second QWs, all of said at least three second QWslocated between the second and third nodes.
 17. A laser system accordingto claim 16, wherein said at least three second QWs are separated fromone another substantially non-equidistantly.
 18. A laser systemaccording to claim 1, wherein a reflector of the optical resonator has areflectance exceeding 99% at the first wavelength, said reflector beingone of a distributed Bragg reflector and a simple reflector.
 19. A lasersystem according to claim 18, wherein said optical resonator furthercomprises an output coupler configured to transmit radiation, generatedwith the gain medium, outside the optical resonator, wherein saidreflector is in integrated with the semiconductor gain medium, andwherein said laser system contains a space between the laser chip andthe output coupler.
 20. A laser system according to claim 1, whereinsaid standing optical wave has third and fourth nodes located along theoptical axis, the third node located within a space occupied by areflector of the optical resonator, the fourth node located within thegain medium, said third and fourth nodes being immediately neighboringto one another, wherein said gain medium includes a second MQW unit,said second MQW unit containing at least one second QW, said second MQWunit located between the third and fourth nodes, and wherein the pumpsource is configured to pump energy to the gain medium to produceexcited carriers in all MQW units present in the laser system.